Much like getting a home under control requires you to control what comes in, I think the first step is coming up with a system to use going forward, one that makes sense for how you instinctively want to look for things. For some that means tagging things extensively, leaving it all in one or two vague folders and using Search to find it again. For others it means a detailed hierarchy of folders and a file naming convention. Maybe a note-keeping application that can handle images/attachments and/or a web-page saving tool if they make up the bulk of what you save. Once you've nailed down the system, you'll have an idea of what you'll need to sort out the backlog.
If you never actually look for things, it's worth re-thinking whether it needs saving in the first place.
My work life I keep in a program called CintaNotes, but that works for me because my "personal" stuff is a lot of code/query snippets and backup copies of reports saved as attachments to the notes. Everything else needs to be kept in the organisation's SharePoint which has its own rules.
For those of you interested, I organized my notes using a program for Windows called CintaNotes. If you can download and install the program, then I'll upload my CintaNotes database to Dropbox or something and PM you the link, and then it would be simple to open it and navigate it within CintaNotes.
Man, looking at my notes again makes me miss the fun of maintaining the database and adding new WoB. If only I had time to keep working on it...
I completely empathise with hating how document handling works in Teams! Though you can make it default to opening files "in desktop app" most of the time, which does help. Doesn't always work, of course, which is why I sync everything to my laptop and access it that way instead despite that not being the "encouraged" approach at my job.
From that description I can see how it turned into a mess! I'm guessing you have a lot of "many-to-many" relationships between categories, so it doesn't lend itself to an easy folder structure, in which case I'd probably go with folders by year (calendar or financial depending on job/company) and tagging for searching within them. Which can be done natively in Windows, though the implementation sucks so I'd look for software to make it more user-friendly (this page lists a bunch of possible options).
The note-keeping application I use is CintaNotes, though I paid for the "Pro" licence because I use it at home too. The free version is fairly limited and doesn't include the truly useful stuff, but I've not been able to find a better application for my use-case (free or paid) than the pro version so for me it's a bargain. The search and auto-tagging rules are excellent, along with the note title, body text, and tags there's also "remarks" for additional free-text comments and a dedicated hyperlink field that come in surprisingly handy, you can make links between notes... I get very enthusiastic about it, but it might not be a better solution for you than tagging software would be.