In terms of tooling there's scoop[0] which does a lot of the capture part of what you're thinking about. The files it creates include request headers and responses, TLS certificates, PDF and screenshots and it has support for signing the whole thing as proof of provenance.

Overall though I think archive.org is probably sufficient proof that a specific page had certain content on a certain day for most purposes today.

0. https://github.com/harvard-lil/scoop