What procedures do you take to save and archive your games?

I don't, because if that happens either others will have done a more thorough job (because it's something they care about - I have my own obsessive areas that I'm the one doing that stuff for), or if they haven't then I have much bigger problems to deal with (e.g. war in Europe).

Nothing, maintaining a library like that would be too much work. 95% of the time I don't want to play a game more than once and if my chosen store closes I can ethically pirate it. Or maybe the game will be buyable as a $5 retro game 20 years from now.
I have 100+ digital only games on Switch too. That's going to shut down at some point but in the future you'll be able to download NS1.zip in ten minutes and it'll have the entire library. So why worry about it now? Once the switch console batteries all start degrading PC emulation will be the default anyway.

I just keep the installers on my NAS, together with whatever dlc installers, patches and mods I deem necessary. With the current prices of 12-18tb hdd drives it doesn't cost much to keep em there.

With GOG, I just put the installers onto a thumbdrive.
With Steam, I was burning discs using its offline backup tool, but I haven't had a disc drive in my PC for years now. IDK if those can be backed up into a thumbdrive these days... It only allowed CD/DVD images to be created the last time I ever used it.
Tons of my games were owned physically before Steam existed though. Those I just keep in their boxes in my closet/storage bins.
- I just put the installers onto a thumbdrive.
  I hope you're powering up that thumb drive every few weeks. Flash memory will lose charge if left unpowered for too long, corrupting your data.
  
  I usually just leave it in the computer until I need to take it somewhere.

Blu-rays are a viable backup medium for long-term storage
- No bdrot?
  
  I mean, you should always check your backups and make 2 for good measure, but supposedly some of these newer ones are made for archival and claim between 10-100 years. Never trust such claims without verification but if true could be the best thing for archival besides punching bits in stone.

Roms and sailing the high seas

For "rare" games like some of my oldies from the 80s and 90s (one or two that weren't even on the abandonware sites last I checked) I have ISOs I ripped and store on my NAS. Same with stuff bought form smaller/sketchier stores (I am sure it is backed up millions of times over, but think Romero's Sigil).
For gog or steam or whatever games? I just don't bother. The French Monk Incident more or less taught me there is zero chance of maintaining archives of GoG games. Their servers are "fine" at the best of times (let alone when the site is "dead") and they don't publicize when an installer is updated or not.
So if gog or steam or whatever goes offline and I still really want to play... Darklands? Piracy.
- French monk incident ?
  
  Way back at the start of GoG (I want to say year one), CDP did the "joke" of suddenly taking down the entire site except for a text page saying they are shutting down. I forget if they said that people would have 24 hours to back up their games or if they said we were up shit creek, it doesn't matter.
  They then basically said "Ha ha, april fools! But you see, that is why you should buy all your games from us because we are DRM free and you own them". Which... rightfully angered a LOT of people.
  So GoG did a video where a "french monk" (which is really weird since they are Polish but...) apologized and gave away a discount code or something. And in The Witcher 2, an NPC was added who alluded to all this and I think gave away a free copy of The Witcher 1 if you beat him at dice poker or whatever?
  Short term? It led to a lot of us actually trying to back up our games. And realizing that was not feasible because GoG would almost never post changelogs or let us know which installers had updated versions and ain't nobody got time to manually scrape every download page. Long term? You can generally tell who was a "GoG OG" in that we look at ANY "And we are the best site ever because we have no DRM and preserve everything" bit of PR from GoG/CDP because it is painfully obvious this is just advertisement for them.