Just remembered about update nag and supernag.
Both of which only happen, if you went online with the system, without "protection" such as 90DNS (
https://gbatemp.net/threads/90dns-dns-server-for-blocking-all-nintendo-servers.516234/). Use this DNS preferably.
Update nag is the newer update already having been downloaded onto your system.
You can get rid of it this way:
https://switch.hacks.guide/blocking-updates.html (read fully)
If that doesnt get rid of it, this is the "if nothing else worked" enhanced version:
https://gbatemp.net/threads/how-to-delete-switch-update.499197/#post-7883999 (please get a second opinion on if this works).
Supernag is a "bit" that gets flipped, when the switch is allowed online - that nags you to update as well (second cause), that can be "unset" using this software:
https://gbatemp.net/threads/gag-order-a-fix-for-supernag.505765/ (READ FULLY).
The thing with supernag is, that Nintendo could potentially see, that you've reverted it, and ban you just for that.
Also - if you've been online, and are now getting an update nag because of it, your nand backup will not prevent you from being banned anymore - because Nintendo now probably has records of a more current state of you being online - so once you revert to your nand backup state (and go online) - they will see that you've reverted and could ban you just for that.
90% of people just give you advice from a "you'll probably be banned anyhow" point of view - which makes this whole things so much more managable for idiots who dont read. Next time, use a DNS to block Nintendo getting all the telemetry from your device, flipping bits, downloading updates... You know the stuff you want to prevent?
Idiots guide through this situation is: Just update to most recent firmware (devmenu is not available on 6.0.1 and up, but appart from that, there should be no detriments) and get banned anyhow (if you installed nsps). Then buy second switch for online.
This posting is only viable for you if you _really_ get a "system update available" nag, and not only a game update available nag. Game update available is much easier to solve (install game update as nsp), or ignore (just ignore).