Selfhosted

Thinking about this, the only ancient information we are still able to access is painted or edged on stone or clay. How about some sort huge wall with thousands of QRcode like engravings?

Tape. Amazon glacier if you're okay with that.

And regular test restores. An untested backup is not a backup.

But when considering what I need to back up, I usually overestimate how much I or other people will care if it's lost. Family photos are great, but what are the odds of someone saying "damn I wish we still had two dozen photos of that one barbecue?"

For your amount, just an external hard drive attached to a NAS or something is fine, or a 2-bay synology would be more than enough. Drives are coming in 20-24TB models now, that'd keep you going for a long time.

The other thing is if I get hit by a bus and no one can work out how to decrypt a backup or whatever.

Documentation, documentation, documentation. No matter what system you have, make sure your loved ones have a detailed, image-heavy, easy to follow guide on how restorations work - at the file level, at the VM level, at whatever level you are using.

That being said, DVDs actually have quite a short shelf life, all things considered. I'd be more inclined to use a pair of archival strength USB NVME drive, updated and tested routinely(quarterly, yearly, whatever makes sense). Or even an LTO tape, if you want to purchase the drive and some tapes.

You can put your backups in something like VeraCrypt. Set an insanely long password, encoded in a QR code, printed on paper. Store it in the same secured location you store your USB drives (or elsewhere, if you have a security posture).

You may also consider, if money is not a concern, a cloud VPS or other online file storage, similarly encrypted. This can provide an easy URL to access for the less tech-savvy, along with secured credentials for recovery efforts. Depending on what your successors might need to access, this could be a very straightforward way to log into a website and download what they need in an emergency.

USB hard drive? If we're talking about a cold backup that's easy to access a USB drive is reliable and easy.

I believe M-Disc to be the best consumer grade, optical solution out there. If you want to go commercial grade you are looking for LTO tapes, but your costs begin rising exponentially. If M-Disc claims are to be believed, they should last well longer than your requirement and be able to handle your data footprint using multiple, but not an unreasonable amount of discs.

No matter which solution you choose, if you are targeting multiple decades, you must save not only the media, but ideally the drive, computer and software used to archive. There is no guarantee that any of the existing technology will be relevant or backward compatible across several decades.

I'm thinking of using a HDD and keeping it at work, which is climate controlled. I'd bring it back every few months to sync the latest.

Since it's constantly being used, I'm pretty confident it'll be usable as a backup if my NAS fails, so it only needs to be "shelf stable" for a few months at a time. If you're retired or something, a safe deposit box at your local bank should do the trick.

In your scenario, I'd be looking at ZFS or BTRFS for your live data, especially when taking photos into account. They'll self-repair files that may run into decay issues, which I've seen a lot of with photos in all formats. Since you already keep off-site backups, I'd then just keep an extra drive around that you snapshot to from time to time.

This is why I do my first-level of backups with rsnapshot. It backs up to the plain filesystem using rsync and uses hard-links to de-dup between backups. No special filesystem, no encryption, restore is just an 'rsync' away.

ZFS with automatic snapshots and scrubbing. This will keep as many and as old snapshots as your like. It'll ensure the files don't rot. It'll ensure the media doesn't die, so long as you have enough redundancy and you replace disks as they die. This is what I'd trust for long term storage because I think I understand how and why it works. It should last as long as I feed it disks. If I delete something, I should be able to restore it from a snapshot. The hardware doesn't need to be anything fancy. Just a Pi 4/5 with a couple of WD Elements would be fine. Could add more disks for more redudnancy. I'm running 2-disk residency.

You don't have to touch the software if it's not exposed to the Internet. Whatever works today on it will work 20 years from now, so long as the hardware works. A couple of spare Pis, SD cards and power supplies should let it last for decades.