Hi Julian.
At ADA, we have a test instance that the ADA devops uses as an initial test to see what might go wrong in an upgrade. It's a pretty bare bones instance and not that complex so nothing usually does go wrong.
Once that test instance has been upgraded and any technical problems identified, the devops upgrades ADA's staging instance which is pretty close to ADA's primary production instance, but not identical.
The ADA team then looks at the release notes to see what optional new functionality is available in the new release.
For any new functionality that is of interest to ADA, a shared spreadsheet is created, the functionality of interest is added as a line, and allocated to the appropriate ADA team member to test it to make sure it works.
Once the list is created, I ask the devops to enable the identified functionality on the newly-upgraded test/staging instance.
For new functionality that is not optional, a line is added to the shared spreadsheet and assigned to an appropriate ADA team member to test it, to ensure it works.
The testing takes place over a week or two based on people's workloads, marking the spreadsheet with P/F and any notes.
Once the testing is complete, I look at any tests that failed and evaluate if we should upgrade ADA's primary production installation or wait for the next release. (We are often 1 release behind the newest, to see if there any bugs identified, and wait for the fix if necessary, then upgrade).
Once everything is deemed ok with the staging installation, the ADA devops upgrades ADA's primary production installation. It is more complex than the staging site so things can still go awry but we upgrade on a Monday or Tuesday evening, so we have the rest of the week to catch anything problematic, rolling back if we have to (although that has been very rare). Ideally everything is re-tested on the production instance, logging issues with the dataverse team for anything that looks like a bug.
I hope that helps... let me know if you want more details on any of the above.
Marina