Military/ War Shooter games recommendation

Have you played Wolfenstein: New Order? I recommend playing that first, even though Old Blood is meant to be a prequel.

You should check out the FPS Legends bundle on Fanatical, Enemy Front looks nice ;)

You definitely need to check out Arma 3, and the rest of the series. The storyline(s) is pretty good, and in A3, the workshop mods and mission are pretty much endless. I bought it intending to play the campaign (I had already watched some of it previous to purchase), have sunk over 600 hours into it, and have not even touched the campaign(s).

Also, consider Bioshock Infinite. If you don't mind shooting arrows instead of bullets, try out Mount & Blade: Warband.

Hah, I clicked on the thread in hope of mentioning Spec Ops: The Line. :D
Hmm, give a go to Homefront and Homefront: The Revolution.

Well,there's Brothers in Arms,Sniper Elite,Medal of Honor,Red Orchestra,old Wolfenstein...

have you tried this?
https://store.steampowered.com/app/212630/Tom_Clancys_Ghost_Recon_Future_Soldier/

a bit old but i enjoyed on my x360 back then

Haven't played it yet, so I can't tell you if fps part is good enough, but System Shock might be worth trying.

My favourite military shooter is red orchestra 2 but keep in mind its a realistic mp shooter.
I can also suggest sniper elite series, insurgency, day of infamy, metal gear solid v, splinter cell blacklist, binary domain and homefront the revolution.

Tried Operation Flashpoint (Dragon Rising and Red River)?

Recommend the Delta Force series, Brothers in arms if you like WW2 tactical shooters, or my personal favourite game of all time, Hidden and Dangerous 2. How old or new the games you are searching for btw?
https://store.steampowered.com/app/32670/Delta_Force_Black_Hawk_Down/
https://store.steampowered.com/app/19800/Brothers_in_Arms_Earned_in_Blood/
https://store.steampowered.com/app/703320/Hidden__Dangerous_2_Courage_Under_Fire/

Try finish great game Wolfenstein Enemy Territory ( ͡º ͜ʖ͡º)

NecroVisioN and NecroVisioN: Lost Company.
But steam versions are bugged, try GOG instead.

Medal of Honor: Airborne was really good at the time (at least in my mind).

I'm currently in love with Escape from Tarkov, not a story driven game really, but a game like no other.

I came to say spec ops the line. You're already on it. Well, I'm out.

https://store.steampowered.com/app/735580/1111_Memories_Retold/
https://store.steampowered.com/app/779340/Total_War_THREE_KINGDOMS/ (Not sure if this counts?)
https://www.ea.com/games/army-of-two/army-of-two-devils-cartel ( Not on steam sadly but a great game)
Wolfenstein Series?
Sniper Elite Series?
Metro Series?
Crysis Series?
Tom Clancy's Ghost Recon?
Spec Ops The Line
Far Cry Series?
Since you tried BF so not gonna add it in.

I just finished the trial for The Division and it fits your description well. You're part of some kind of military high tech division and you have to clean up the city of looters, killers, terrorists etc. It has impressive graphics, it runs well, the shooting is satisfying and the story might be good? I don't know yet, it's intriguing at least, from what I played. It was quite fun I'll grab it next sale for 5 bucks. Try the trial if you're interested, it takes 6 hours or until you reach level 8, the progress is saved in case you buy the full game.

Insurgency: Sandstorm, is the best Militar FPS online shooter. Great sound and effects.
Another great FPS online is Risings Storm 2.
For single Player FPS, Metro Exodus and Dying Light
Ghost Recon: Wildlands TPS militarty coop.

Swat 3 and 4 for FPS tactical single player, are old but are very good games.