If left long enough, would a standard computer eventually calculate and increase its depth?
“powerful computers” for chess engines?
If left long enough, would a standard computer eventually calculate and increase its depth?

Not sure but these might be interesting :
https://en.wikipedia.org/wiki/Deep_Blue_(chess_computer)
https://www.youtube.com/watch?v=wljgxS7tZVE

A more powerful computer also won't need to prune as aggressively in order to keep the search tree manageable, so there is less chance of missing a continuation entirely.

PC power isn't that important if you are just analyzing a played game and don't need the output of a what line is best right away. It will give you that answer but may take a minute or two longer to have. As for depth most use 20 so they can find the fastest most direct line. I have read articles from GMs that play on ICCF that they use older PCs that do run newer engine software like stockfish 11 but setup for 4 lines with 20 depth then click refute to determine the best line.

As a quick guess:
More RAM means that it can hold more positions in memory for it to compare with each other. Now, FEN files aren't that big, so it might not make that much of a difference. But, even though it is likely only showing you the few top lines, there's still possibly thousands of different positions (or more) that it is constantly re-evaluating as it digs deeper.
Faster processor/more cores means that it is going to be evaluating those positions faster and is thus able to get to deeper ply that much quicker, which may make the difference between minutes and hours to dig really deep into the positions. A slower computer might not be digging deep enough into the position fast enough to find the best moves in tricky positions during the allotted time.
I’ve heard titled players who are discussing engine prep and theory online/YouTube/streams talk about engines running on powerful computers with multiple cores will produce much better moves... or at least that’s what I think I’m interpreting.
Can someone clarify this?
Would there really be a difference between say, a normal consumer i5 processor laptop with say 8 gb of RAM, vs a laptop running i9, 32 gb of RAM vs running stock fish on your analysis board app on your iPhone?
In terms of humans, surely prep with an engine on your phone is sufficient already?