In general, is it safer to update an out of date Mac “all at once”
just catching up to the latest?
The only real 'risk' in upgrading your OS is whether your existing third-party software will run on the new version. Software that is contemporary with OS version
N will probably work fine on OS
N+1. However, running that same software on OS version
N+4 may well cause issues.
Mac App Store apps will automatically notify you of updates for a new OS; and even install themselves invisibly, if you want. Other software may check for updates; some may even require a paid update. But, you need to check what you have installed, and what the latest versions are.
The things that usually cause problems (rather than just crashing ;-) ) are not apps, but "other things", like drivers, and background processes that have been installed to run silently.
I'd suggest that its 'safer' to keep reasonably up-to-date with your OS -- perhaps stay on Ventura until Sonoma .3, then keep up with Sonoma until the next OS is on .3 -- than it is to do large jumps very rarely; but there's no benefit to 'working through the gears'.