Single miniature rulesets?

[blacksoilbill]

Pulp Alley would do the trick. It has rules and mechanics that facilitate non-combat actions. It also does have a solo option, but I don't think you'd need it if all the players are on their own side.

[since1968]

It takes place in a large building with lots of rooms and people wandering around (ex. museum). Each player controls a KGB spy. They don't know the allegiance of the other spies.

Black Ops covers your requirements:

https://tinyhordes.com/osprey-black-ops-review/

[Flinty]

I've often dabbled in this sort of game - Inquisitor was a good suggestion and you might want to look at Warwick Kincade's Normandy Firefight.

arwickkinrade.blogspot.com/2011/12/sneak-peak-normandy-firefight.html

I found that what would be excessive granularity in a typical skirmish game - character pose, ammo counting, actions etc, can be really immersive without slowing up the game, or more importantly, becoming tedious. I think NF manages to pull this off really well.

Inquisitor is a good base, it has a nice activation sequence based on a characters initiative, but after a while comes across as a bit rushed/rough round the edges - I found there was a huge tempation for players to tweak the stats or indulge in powerplay, which was even encouraged by Gav Thorpe, but if rigourously controlled, it can produce some really interesting games .