Brace for something a little harsh:
So I was expecting classic Tomb Raider, but the jumping doesn't feel all that momentum based and doesn't quite nail the thrill of leaping large gaps. Not to say that it needs to be, but when the character auto grabs the ledge instead of wanting to jump off of it, there's a problem and this was a constant throughout. You could argue that it was the intent to go for Modern Tomb Raider, but the issue is those games don't really pride themselves on "jumping puzzles" as much unless you count "spot the white highlighted edge" as the same gameplay. Point is, level design feels like a classic tomb raider, jumping feels like an awkward modern raider, the two things don't mix well together.
The atmosphere doesn't really quite hit the mark either. The looping music really dulls the experience as opposed to implementing soundscapes and putting in musical ques for when you reach a new area or something significant happens. There's not much contrast other than the boulder scene inserting new music. It helps to rely more on ambiance and noise, and use music when necessary for an emotional change or discovery.
I also feel that getting to the series of ledges at the top of the first area to activate (the starting platform I think?) could have been more interesting to backtrack from. Instead you had to shimmy across the very ledges you climb up to. I really don't think wall climbing is that fun unless there's some kind of risk or thinking to it, instead they're just spammed along the wall to create filler and busy work. Not only that, but there's no way to jump down as a neat little shortcut, instead you pretty much die. Although by accident I managed to survive a fall near the secret green object (I assume that's optional). But I noticed a trend in a lot of games when they program ladders, it's always faster to go down them then it is to climb up, it's an interesting design philosophy that I think could have been used more here. When someone wants to go snow sledding, they wouldn't want going down hill to take the same time/effort as going uphill. That's kind of the logic I'm going for here.
Roll doesn't seem to do anything, and I got through the spinning blade section without really crouching. The timing puzzles before the boulder were pretty annoying. In old TR games they're usually timed in such a way that you'll get through them as long as you past the first one, but the obstacle usually isn't just the swinging blades but rather the crumbling floor or some other element that forces you to improvise while having to constantly run. Having to stop in-between each blade was pretty frustrating, and the timings were rather unforgiving. Again though, had a lot of issues jumping between the ledges in that section (where my character kept constantly grabbing it).
Overall there were a lot of movement glitches and odd behavior throughout. Kind of dulled the experience more. I thought the art-style and lighting was okay, but I've seen a lot of stuff like this before in unity. So I don't really have a glowing opinion on it. Sorry if this is all very negative but I'm pretty passionate about the old Tomb Raider games. And although I think the modern tomb raiders are fine, I do desperately want a return to old form. Mirror's Edge is the closest they got to that, but then the sequel went open world for no real good reason.