These are definitely thought-provoking questions and there are branches of mathematical philosophy such as constructivism and mathematical intuitionism that explore these.
Even if computation is not directly part of the laws of physics, knowing that humans and our computers are limited to things that are finite and computable might place limits on how we can appreciate how the universe works.
This is kind of a digression but if you (or others) are interested in some examples of things that are right on the edge of these questions you should check out the [busy beaver function](https://www.quantamagazine.org/amateur-mathematicians-find-f...). This tell you the maximum number of steps an n-state Turing machine can take before halting.
Even if computation is not directly part of the laws of physics, knowing that humans and our computers are limited to things that are finite and computable might place limits on how we can appreciate how the universe works.
This is kind of a digression but if you (or others) are interested in some examples of things that are right on the edge of these questions you should check out the [busy beaver function](https://www.quantamagazine.org/amateur-mathematicians-find-f...). This tell you the maximum number of steps an n-state Turing machine can take before halting.