What medium should be used for long term, high volume, data storage (archival)?

Best medium is paper, but that's difficult to do for high volume. OTOH, maintaining archives is much more work than generating the copies, so it pays to keep volume as low as possible.

I keep paper copies of really important stuff, in addition to archiving them on other media. Most other files go onto M-Disc Blu-Ray discs. Even though I'm skeptical that M-Disc is worth the premium, I'm gambling that it's at least as reliable as regular Blu-Ray. I also encrypt and upload tar balls to rsync.net, but key management is anxiety-inducing[1] and I've been doing that less and less. (I've been doing this since before tarsnap existed. I'd probably use tarsnap if I was starting from scratch.) I also use Time Machine, but manually every few months, and that's only one desktop, which happens to two hard drives.

Once Git took hold 10+ years ago I began maintaining some folders as Git repositories. In addition to properly versioning stuff, it's much easier to move data around using git push and git clone. Some close friends and I have been running our own co-located physical servers for close to 20 years, so I'm comfortable pushing unencrypted data onto such a remote server, whereas I would never think of pushing unencrypted data to a service or VM, no matter if they claimed to encrypt it.[1]

Whenever I upgrade a personal computer or personal server I usually save the hard drive in storage, but I'm not sure it's worth the effort.

I don't archive multimedia, except for family photos. The maintenance burden of archiving movies and music isn't worth it, though I never enjoyed collecting multimedia as much as others.

That's my process, which largely developed organically rather than deliberately. Everybody has their own process but it's always useful hearing about the details.

[1] Remember, key management is always the achilles heel, both short-term and long-term. Focusing on details, like AES-128 v AES-256, is often counterproductive in terms of navigating the solution space. Likewise, whether PBKDF2 or Argon2 is used for generating a key is irrelevant to me as generating a key from a memorized password is, IMO, a losing proposition from the start.

Glacier or similar service.