I think those warnings are for the overly cautious. Certainly we have never waited for all jobs to exit before upgrading. Out of paranoia we pause all our jobs, but that is not required. Typically you can upgrade between versions without pausing or canceling jobs. That said you will want to look at the release notes and changelog for the version you want to upgrade to in case there is any issue that is flagged that requires more paranoia. Generally minor version upgrades are fine.
The thing I would note though is this phrase "Any jobs started before the slurmd system was upgraded will be running with the old version of slurmstepd, so starting another upgrade or trying to use new features in the new version may cause problems." What really this is noting is that upgrading in quick succession (especially major upgrades) could be problematic. So say you were to go from 22.05.3 -> 23.11 and then immediately go to 25.05, that could cause problems. If you intend to go from your current version to the latest I recommend spacing out the upgrades, or taking a full downtime.
That said I have never done an upgrade over that large a version change so some one with more experience on the list should be able to answer any questions related to that. My gut says though that if I were trying to step to the latest version I would either clear out the existing jobs, or I would do one upgrade per week to give the jobs on the cluster time to adjust to the new version.
-Paul Edmon-