Old Win 10 PC died, can't find Licence Key

Had my almost 10 year old desktop killed by a power surge, PSU and motherboard were fried. I've tried finding the licence key on the still working C: but no luck.

Having a new desktop built and Win 11 is being installed (not buying a licence). If I log into my Microsoft account on this new machine will it automatically licence itself?

When I log into my Microsoft account it doesn't show that I ever purchased Win 10.