Magic user capture and containment procedures

In the same world where magic is commonplace enough to warrant deterrents..... Aren't anti magic fields just as likely or common?

witches and other magic users are a not uncommon threat, not as common as say the street gangs but common enough to have dedicated witchunters and inquisitors plus the guy who gives you said ninja cthulhu magic loves to dick around and give people magic for shits and giggles.

Have the good magi use binding and surpression spells to prevent them from casting.

Oh hell yeah it's rare. Hang on, dredging this up from my memory.

The Outsider gives out his Mark to those who interest him, though never more than half a dozen or so at once. Not sure if that's a mechanical limit on his part or if he just doesn't want to.
Thing is, it's not just those with his Mark who can do magic. Doud, the assassin he gives a mark to found he could give his other assassins a portion of his power, thus his entire faction could Blink. Plus some people like Granny Rags and likely others gain power through the Void or the Outsider in other ways, and it's likely that bone charms and runes have SOME effect, even if she that is beyond going a little bit insane is hard to say.

So there is magic everywhere in the dark corners if you know how to recognise it. Just not often flashy and more creepy bone pieces, plus dreams.

The Overseers have the counter 'music' after one of their own dreamed of the Void -and almost certainly came in contact with the Outsider- and... learnt it's song?
It was a little vague, but he then applied a few mad math things to it and came up with a counter-song, and likely did occult shit too as the Overseers still aren't sure how exactly the music boxes work, or even if they are magic themselves.
But because they work most of them aren't willing to look into the matter.

The Outsider dicking around with giving people powers is fairly rare, though, there are only 5 or 6 people in the entire world that have his mark at the time of Dishonored.

Those who become Espers require a great deal of augmentation followed by routine medical examinations and check ups. essentially becoming an Esper means you have a doctor for life who was there before, during, and after the surgery to augment you.

You could go rogue, but then when you fuck up and cause yourself to go into cell death you have yourself to blame unless your doctor decides to go rogue with you, and even then you need facilities and equipment to maintain your body and powers.

your right granted the outsider only gives out his party favors to a select few but he influences the world in more ways like appearing in Piero's dreams or the cults that spring up trying to earn his favor. the point is he dicks around enough to make it so the overseers actually have a purpose.

To be fair, he doesn't seem to really be interested in the cults. They just happen and he occasionally looks at them, sees nothing of interest and goes back to fapping to Corvo along with his weird icy void snake friend.

I have this setting where a magical war between two magocracies went out of control and destroyed a continent. Afterwards, all magic is regulated by a geneva convention-like treaty called the Marnaka Treaty, and an organization is built specifically to detect, catch and persecute rogue magic users.

Basically the rules set by the organization boils down to these:

1) No use of virulently contagious magic, especially if damaging.
2) No use of mass necromancy.
3) No use of heavy mind-altering magic, especially en masse.
4) No summoning of gigantic or legendary beasts or entities without the proper safety protocols, or consent of said creature if sentient.
5) No use of magic that alter the essence of a race or sentient considerably.
6) No use of instant-kill magic.
7) Other new forms of magic should be presented to the Grand Mages' Jury in Marnaka for consideration and ratification.

There is an organization made after the treaty was signed, the Oathsworn Enforcers. They are made up of mages and non-mages alike, who utilize anti magic artifacts to neutralize offenders. They're largely undercover, but when they lay down the hammer they do it effectively.
The Oathsworn organization itself is composed of 3 parts: Enforcers, Agents and Justicars. Agents are the ones who sniff around for signs of illegal magics, and confirm if it's the case. Enforcers are the ones who are sent to deal with it, by negating or nullifying the magics, and/or capturing the perps responsible, securing and if need be, destroying any illegal magic artifacts. Justicars are the ones who prosecute the perps, locking their magic, and bringing them back to Marnaka to be judged. In some cases they also negate and nullify the perps' connection with magic as well.

5 or 6 in the world in that one geographic area. That we know about.

Wouldn't magic-users be aware of these groups, and either toe the line, or take precautions against them?

Obviously, you do that with the regular police why wouldn't you do it when they practice how to shut you done when they've caught wind of your prostitution ring composed if kidnapped girls and children and brainwashing them so they can be used.

In my campaign, we rounded up all demographics with high magic user frequency.

We got the liches and told then that their phylacteries would be stored for their own safety.

The phylacteries got smashed by hydraulic presses and I was banned for writing this

A functional legal system coupled with an understanding that no extra effort will be made to take magic users alive. And by that I mean a very steep use-of-force continuum.

If they come along quietly things actually get straightened out. Resist and find out that being simultaneously hunted by the guards, the church, the Mage's Guild, and anyone else interested in the cash reward isn't much fun. And Gods help you if you piss them off bad enough to get a Red Notice issued in your name.

A lot of bounty hunters get pretty good at rogue mages because the money is better and there's no chance any questions are going to be asked about excessive....well, anything, really.

Every once in a while one of the guards will drag in (usually literally) a mage with two broken hands and a busted jaw but it's pretty rare and somewhat frowned on. The Captains generally figure if they're putting up enough of a fight for it to get that bad it might as well be a completely lethal force situation and be done with it, but most guards won't turn down an honest surrender that late in the fight.

(As Judge Dredd as all this sounds, it's actually a pretty high-magic, fairly noblebright setting. They just take a real dim view of threats to public safety.)

One cannot fight mages with technology alone, for Mages are clever sorts, and even those without use of elemental lightning magic can find creative applications of their magic to shut down your team.

To this end, Anti-Magical-Terrorism Units are formed. Operators are kitted out with magitech gear, armor, communications, and weapons, rendering Magi jamming techniques useless. They've even got the lab warlocks charging canisters with magical effects, to act as magic grenades.

Having trouble clearing rooms because your target is a pyromancer, effectively giving him a man-portable flamethrower? Just before you enter, toss in a freeze grenade, coating the whole place in a lovely little layer of frost and dulling the target's powers for a time.

Need to quickly scale a building to reach a target? Teleportation grapnels will get you up there in a flash.

Basically, Magic Version of Rainbow Six Siege.