Well, one can go on discord and search existing channels for a specific game, so it can be found in a casual search if one knows to look within discord. And the search tools within a given channel are pretty useful.
Regarding what happens if discord goes "tits up," well, that could happen anywhere on the internet - I'm lookin' at you, slick productions!
I will say, though, I have no clue how it has managed to stay afloat. It has no ads, doesn't charge for membership, and AFAIK it doesn't cost to host a channel.
Nowadays between archive sites, personal archives and things being cross pollinated then while things could be lost it is not as great a worry for plain old web.
"if one knows to look within discord"
That is almost as bad as facebook groups -- I had thought we had all learned that walled garden web was a bad idea back when AOL and compuserv still came on floppy discs but apparently I was wrong. Though the popularity of proprietary protocol IM services you can't run your own servers, and seeming lack of open ones other than the few crazies still rocking xmpp setups and the continued wonder that is IRC, probably says most of what I would need to know there.
Come to think of it, would things like the SMW Jailbreak or the SMB3 Wrong Warp have been possible in a bygone era, or are such discoveries reliant on more recent software?
The Mario save stuff. Most of the old console save mods or control input driven homebrew demos are more party tricks than anything terribly practical -- emulators, cheat devices and flash carts were commonplace long before then so there was less need for such things.
For the input stuff it is usually a fault condition that sees a game jump to a piece of nominally non code. If they can control the destination or the destination is somewhat user manipulated then the rest is so much abstract assembly, possibly a bit more still if you are having to work around some binary combo not being easily made within a game. Analysing the fault condition can be done with fairly basic debugger tools. I imagine the later prevalence of save exploits and return oriented programming promoted some of the ideas that led to all this but at the same time take anybody that could code in a proper variable width font (not sure of the exact timelines here but it was not a radical new invention of recent years) and find a suitable candidate for said fault condition and I would expect them to make some decent headway if you asked them to do it.
Maybe some aspects of tool assisted speedrunning, however most things there still seem to be discovered by accident and then refined. Even then savestate editing will probably get you most places there, even if it takes a whole weekend to do what might take a few hours with a full bore Lua supporting TAS focused emulator.
I like big data approaches*, I like things wherein we see a neural net playtest something or exhaustive input done by automated program. Haven't seem individual hacks benefit really, just things where people find oddities. Similarly have not seen some kind of great leap in mindset or abilities. More hackers, possibly even more up for a bit of assembly fiddling, more polished tools able to change more about a given game and more documentation but not great leaps in ability or technique, or tools that somehow increase base level (how many high school athletes today with modern gear and training would do spectacularly in the 50s or something?) or were the results of some unexpected skills/serious investments/crazy discoveries.
*choice link of marginal relevance here but probably of general readers of this forum https://towardsdatascience.com/tagged/gaming?source=post