Is it possible to set up that all Snaps will be automatically updated as soon as the computer is started (so that I don’t have to open the Snap store first and do this manually – search for updates, etc.)?
I imagine it to be similar to the “normal” Software Updater.
Well, snapd checks for updates 4 times per day by default and if there is anything to update it will quietly do that in the background without you needing to do anything…
Beyond this you can set up a schedule instead of the default setting so it only checks when you scheduled it …
Something like “update immediately after boot” does not exist and IIRC there is even code to avoid updating right after boot because that can slow down your system start if it happens too early…
You could manually create a systemd unit file that calls snap refresh as a oneshot daemon after the graphical target is reached though…