Played the demo, got some feedback.
In terms of basic movement and aiming the game feels decent. The walk speed is a decent clip, and I can tell there's a little autocorrect in the aim but its not obnoxious. Its clear some effort has gone into polishing the basics.
Sound is reasonably good, but its a little too retro - the scratchyness of the audio makes it tough to tell what the guys are yelling, even if its random curses in German.
Enemies are fine as standard mooks. The AI is a little weak, but its right on the level of what you would do for a standard cannon fodder mook anyway so I wouldn't worry about improving it too much until you get to the later stages where enemies are supposed to be more challenging. Try not to fall into the "more health/damage = higher tier enemy" trap. That approach only gets you so far because in order for them to work you have to have really empty levels so they don't get stuck on shit, and you end up with really boring level design. The animations for attacking and dying are solid though, and aside from potentially adding additional intermediate frames they don't need to change much.
You gotta tighten up your roofs and add a deathfloor outside the map for sure. I was testing wallrunning and I hit a rafter, popped out of the map, wandered around a bit and tried to jump to my death only to fall eternally.
Speaking of wallrunning, its a neat idea to work it into a Wolfenstein/Doom style shooter, but you need to spend a bit more time figuring out how to make it feel a bit more natural. It can be activated by accident by jumping with a wall to your back, and its really easy to just keep doing it forever. Maybe check out the Prince of Persia Sands of Time series for an idea of how to make wallrunning feel good in the physics engine, and how to limit it while keeping it fun. As it is, when I tried to wallrun around and shoot the bad guys, I was moving way too fast to aim, they had no problem hitting me, and I kept getting hung up on rafters and shit. In first person its easy to not even realize you're doing it as well, because there's no real change to speed or trajectory so you just kind of float around walls randomly while playing sometimes. This came to my attention when I tried to jump on a table to try to pick stuff up and instead I flew past it and shot around a corner. Also the instant directional change on wall corners is really disorienting.
You should look at games like Doom for cues on your HUD. What you've got is functional, and the drawings on the main character look good, but you picked a font thats pretty hard to read for ammo and health, and its nice to have an indicator of what/how many weapons you have on hand.The trenchgun and pistol look really similar so without a HUD indicator its tough to tell what you have equipped until you fire.
I think all that is pretty standard for an early demo like this. I can see where you're going and there's clear effort being put in to get stuff to work, you just need to spend a bit more time workshopping your mechanics and playing with the physics engine to tighten up. Remember that level design is half the game, so if you want to have something like wallrunning, you need to design levels so there's fun stuff to use wallrunning for in the primary gameplay loop. The primary loop is shooting nazis, so you need to work wallrunning into shooting nazis.
Aesthetic -wise, I think you're gonna have to depart from the classic look you went for a bit. Your synopsis above says that this is 2025, but the masonry and rafter design hearkens back a century earlier. Being nostalgic for the 1940's is one thing and can be argued away for your enemy dress style, sleeping in a damp smelly masonry building is another. I know you're going for the evil nazi throwback look, but we don't build structures that way anymore and haven't for decades, and most people would wilt at the prospect of sleeping in an era-appropriate castle - you can't run ethernet cables through stone masonry walls. You don't have to go for futuristic chrome on every surface, but it will work against your story if your visible setting is so displaced from the written setting.
If you want a modern look that comes across kind of wrong look up McMansions, and if you want something sinister check out photos of experimental architecture. Its not all bad in either case, but you will periodically come across photos of structures that will make you feel uncomfortable. The blog "McMansion Hell" is really good for pointing out stuff that makes a structure unattractive/wrong feeling that people typically 'feel' rather than 'see'. Intentionally designing structure interiors/exteriors 'wrong' can help bring across a feeling of uneasiness/badness in a modern setting without having to resort to the bludgeon of the damp castle dungeon.