Know I'm kinda late to the party, but in the hopes that this project is still under development, I thought I'd give some feedback :)
Just finished my first and only run (after the tutorial) in the second loop after encountering a bug that stopped me from progressing. I used the "report incident" shortcut (F8), and hope you can find the cause. Despite the abrupt end, I had a good time!
First off, my biggest concern is the lack of strategic importance put on positioning (at least when playing paladin and mountain). I realize this might be rooted in a balancing issue, but I hardly ever used move cards at all, and after the first loop, I got rid of them. The enemy will swarm at you regardless, and having a bunch of cards that can't deal or mitigate damage is simply a handicap. In addition, I got one upgrade that gave me permanent cover, and another that gave me dashes every turn.
Secondly, I never had a man down (though I obviously never got that far), but I can see how that mechanic could potentially be frustrating. It means struggling players will have a harder time from then on, with the odds gradually stacking up against them. Considering how few and weak your options of healing are, I'm guessing it's pretty likely for the same character to die repeatedly (as they are only revived with 5 hp)
Thirdly, I think the virus mechanic is really cool, especially how their severity scales with how much power they take to get rid off, but I found that I would often spare the last opponent in a room just to wait until I could remove them. This is somewhat reminiscent of healing with certain deckbuilds in "slay the spire" which you mention as an influence, but I still think it can become a chore. Without the experience to back it up, I also think it will be strategic to just get rid of all your bad starting cards in the first, easiest loop, where the handicap of a virus is manageable, but I don't think that's the most fun way to play. Maybe make the power-cost decrease per room/battle instead of per use?
Fourthly, a couple of ui-issues: As someone else just mentioned, there are several points where I get a prompt to make a choice, and can't look at my decks or upgrades. I might just be spoiled after "into the breach", but I would also love some way of checking the enemy turn-orders (though I can see how this could be a little too "gamey"). There were also a few times where I wanted to check the AOE of a card, but had to make the power for it first. I think it would be nicer if you could select a card, even if you can't afford it.
Fifthly, I think the shield-mechanic is interesting, but has a few problems. It's already a bit weird that the shield you get from cover stays with you once you leave it, or that it helps you against attacks from behind, but once I got used to that, it didn't bother me. The real problem is scaling, and how after just one loop, enemies started dealing so much damage that the 3 shield you got from cover is almost negligible. It ends up as sort of a wasted mechanic with little impact. Maybe increase the amount gained from cover per loop? Also, the fact that almost half of the attacks that hit me would deplete all the shield I had, regardless of the amount, and how this obviously led to the "armored" status-effect just to counter it, is a bit clumsy. It makes going for a shield-build seem unreliable. Maybe remove or reduce the amount of shield-drain enemies, and make shields slowly deplete per turn instead?
Sixthly (are these even words anymore?), I think character-locked upgrades is frustrating. Several times I leveled up and got new upgrades, just to find that both characters got the one I wish I could put on the other, rendering them nearly useless. Especially since you have the upgrade rooms where you actually do get to choose as a comparison. One of the great joys in any tcg or rpg is the feeling of optimizing your build, and this made them feel clunky and imperfect.
Seventhly, I was a bit confused on this point, but I believe you only draw cards up to your hand-limit every turn. This means you are sort of punished for not spending all your cards, because you'll draw fewer in the turn to come (allowing you to play fewer cards overall). This incentivises individually strong cards instead of synergies (which are more fun in my opinion). There might be some aspect to this I haven't realized, but otherwise, I would heavily suggest to just allow the player to draw a set amount of cards, the delayed turn is punishment enough!
I'm not going to delve into features that are just a matter of more content, like more diverse enemies or interactable objects on the battlefields, but I do hope you make the card-pools character specific (the decks of my paladin and my mountain ended up very similar).
I also wanted to mention the theme, even if it isn't strictly criticism. I think what you touch on with the viruses and the sci-fi tech like teleportation is really cool, and I'd love to see this game take that matrix-esque direction. I'm personally a bit put off by the "modern warfare"-aesthetic, and I also guess some of the more lacking mechanics and designs are pulled along with it. I'm not suggesting to make the whole dungeon a simulation or anything (though saying that, it does sound cool), but it's something to consider.
As someone interested in game-design, I had a lot of fun writing this out, and if you can find some use for it, that would just be an added bonus!
PS: Sorry for the long comment!