What advantages should a 2500 years old vampire have?

i read it as
you're terrible but what you just posted was even more so

Van Richten's guides are Great!

This picture sums up how I see it.

The most dangerous thing of all: Patience

Also they could lose all sense of scale. I'm thinking that "Immortal Elvish Sorceress trying to resurrect her dead human boyfriend" greentext levels here

All of them. Any vampire that's been alive that long will be more like a god than anything else.

Can go to an antique shop with his living room and make millions

Leader of a cult which terrorizes north america and europe. Think of Tokyo Ghoul.

Functionally infinite wealth. Maybe even literally infinite amounts of currency, like the Rothschilds in the /pol/ memes about them owning the Federal Reserve.

Political contacts that would make the Freemasons and Bilderberg Group look like a college activism club.

Incomparable knowledge of all subjects, to the extent that even a trivial interest in academia over that much time could make him the most knowledgeable person in the world in most fields of study.

The ability to cast Mortify and to create Angels.

Advantages huh? So we're talking GURPS then? If you aren't, this might at least give you a nice direction to look in for further inspiration. If you are, you still may need to figure out how to convert some of the specifics of the things mentioned to the edition you're playing if it's not 3rd edition.
So you have a fair number of choices, but you might want to look at the GURPS Vampire the Masquerade and VTM Companion for 3rd edition for inspiration, bearing in mind that vampires that old are at most generation 7, probably earlier, meaning your vampire will have a huge reservoir of power and likely have a discipline at 6+ levels, providing very high power abilities and a wide selection to choose from at each level.
Obviously a vampire that old would be very tough and very clever, so high HT and IQ. This vampire probably has many 'children', so he has (potentially double-crossing) allies, contacts, and potentially very high status. To interact with the human world, he either has tremendous wealth and a great ability to blend in or a subordinate with tremendous wealth to handle that for him. It is likely that very few individuals, vampire or otherwise, will interact with your ancient vampire directly.
Altered time rate and extra attacks of some variety are always good for combat, as well as combat reflexes. Anything to increase durability may be worth having as well, such as some flavor of damage resistance/reduction. Consider alertness, charisma, and other things suggested in the GURPS VTM book as well.
Most of the advantages that vampirism implies are covered by the GURPS VTM rules as a 55 point template, including Unaging, Blood Healing, Doesn't Breathe, and Vampiric Invulnerability.
Lastly, consider some more unusual abilities like afflictions and ranged attacks, such as a freezing attack, or eye lasers if you're into some more unusual fare.

Patience.

Knows all the good memes from 2485 years ago, and can share them with any of his friends from then that haven't been staked.

mecha-gregole.deviantart.com/art/13-Spooks-The-Vampire-King-410784483

No more fucks left to give.

I always thought of higher age as upping their defensive capabilities in the main. Probably the means to kill them becomes more and more obscure and specific, likely tied to their history ala Strahd.

In the Guilty Gear universe, the one known vampire took an interest in seeing the growth of humanity through the ages and sought to guide their growth in some fashion, so he created an Assassin's Guild to help, "prune the tree of humanity" when needed.

Then Magic got revealed to the world, and he started chilling out a bit, seeing what happens now that humans have supernatural powers. Oh, he also picked up a human wife that he drains of ALL her blood whenever he gets hungry, and within minutes she respawns and goes about like this is par for the course.

As expected, humanity nearly kills themselves by making bio-engineered magic creatures and plunge themselves into a decades long world war (note that because most 'mechanical' technology became a stigma right around the time Magic became a thing, there's no nuclear bombs and few guns, so most of the war was literally knights and wizards vs. fuck huge monsters).

The entire time he just sits and chills, and starts to grow bored because he wants to fight and cut loose, but if he does so, a whole country probably goes kablooie.

Humans win the war eventually thanks to a bounty hunter killing the commander of the monster army, making the rest go (mostly) inert.

A couple years pass, he thinks humanity is finally starting to become a thing that doesn't need pruning, and helps shut down his own Assassin's Guild with his lieutenants and makes everyone go back to a peaceful life.

... That sounds rather peaceful and well planned, right? Go look up what Guilty Gear is, and the character Slayer. If I wasn't on mobile, I'd post a pic of him.

I got you user. Pic related is how he looks as of the current game iteration.

Note that Slayer is one of the most powerful beings in the world in terms of raw strength. Of of the few desires he has is that he wants to fight the bounty hunter that took down the commander of the monsters in that long world war.

But he knows they probably can't, because if they do so, an entire continent would probably get wrecked in the process.

>-Ghouls, and two means to offsping, Katane and Dhammpirs, with Vampire bloodline class NPCs
Ka-ta-ne or Ka-tayn?

Holy fuck learn to format.

My Dear Young Friends,
How lovely of you to have stopped by!
I am never averse to company; it has been one of my
great joys in a long and often lonely life. Had you come
in the evening, I should have welcomed you in person
with the greatest of pleasure. However, since I
suspected you might choose to arrive during daylight
hours, I thought it best to be out.
I have left you a small token of my appreciation;
someone very near and dear to one of you is now in the
place where I occupied my days until I decided that
other quarters might be more congenial. She is very
lovely, Mr Mears-very toothsome, if I may be
permitted as mall bon mot. I have no further need of herand so I have left her for you to-how is your idiom?
-to warmup for the main event. To whet your
appetites, if you like. Let us see how well you like the
appetizer to the main course you contemplate, shall we?
Master Petrie, you have robbed me of the most
faithful and resourceful servant I have ever known. You
have caused me, in an indirect fashion, to take part in
his ruination; have caused my own appetites to betray
me. You sneaked up behind him, doubtless. Iam going
to enjoy dealing with you. Your parents first, I think.
Tonight… or tomorrow night… or the next. And then
you. But you shall enter my church as choirboy
castratum.

And Father Callahan-have they persuaded you to
come?I thought so. I have observed you at some length
since I arrived in Jerusalem’s Lot… much as a good
chess player will study the games of his opposition,am I
correct? The Catholic Church is not the oldest of my
opponents, though! I was old when it was young, when
its members hid in the catacombs of Romeand painted
fishes on their chests so they could tell one from
another. I was strong when this simpering club of bread-eaters and wine-drinkers who venerate the
sheep-savior was weak. My rites were old when the
rites of your church were unconceived. Yet I do not
underestimate. I am wisein the ways of goodnessas
well as those of evil. I am not jaded.
And I will best you. How? you say. Does not
Callahan bear the symbol of White? Does not Callahan
move in the day as well as the night? Are there not
charms and potions, both Christian and pagan, which
my so-good friend Matthew Burke has informed me
and my compatriots of? Yes, yes,and yes. But I have
lived longer than you. I am crafty. I am not the serpent,
but the father of serpents.
Still, you say, this is not enough. And it is not. In the
end, ‘Father’ Callahan, you will undo yourself. Your
faith in the White is weak and soft. Your talk oflove is
presumption. Only when you speak ofthe bottle are
you informed.
My good, good friends-Mr Mears; Mr Cody;
Master Petrie; Father Callahan-enjoy your stay. The
Médoc is excellent, procured for me especially by the
late owner of this house, whose personal company I was never able to enjoy. Please be my guests if you still
have a taste for wine after you have finished the work at
hand. We will meet again, in person,and I shall convey
my felicitations to each of you at that time in a more
personal way.
Until then,adieu.
BARLOW.