Is there any concept of signing data at time of archive, and verification at time of access, to prove it is not later tampered with, say by a bribed sysadmin?

Similarly are there any general supply chain integrity measures in place, such as code review of dependencies, reproducible builds, or creating archives reproducibly in independently administrated enclaves?

You note archives could be used for instances like Supreme Court decisions, so any anyone with power to tamper with content would certainly be targeted.