What's something that's seen as Obsolete, but isn't?

Magnetic tape. It's one of the better long-term offline backup solutions. It is compact, inexpensive, has no moving parts (bearings, motors, reader heads), no scratchable surfaces, and can last for decades in a moderately climate-controlled room.
Just keep it away from magnets... or iron vaults. According to an anecdote (that I can't find right now), a large bank vault was repurposed as an offsite backup storage, except it kept wiping the magnetic tapes because the thick iron walls reacted to changes in the geomagnetic field.
- We used to do tape backups up until about 6 years ago, but our higher headquarters decided they wanted to go all in on Rubrik instead. I will say that it is a lot easier to maintain and conduct restores from, and we have all of our various sites' Rubriks backing up to each other for redundancy. But you're definitely right that tape is far cheaper per GiB of storage than anything else.
- Correlary: always test your backups and don't just assume that they will work when you need them.

Analogue clocks, particularly clock towers in towns, but also just basic clocks on the wall in your home. With smart devices everywhere, it seems like they're not needed and probably old-fashioned. The circular 12-hour clock face probably feels like the floppy disk icon or the rotary telephone, in terms of how 'of another era' it is, but it's still a fantastic and resilient form factor for the purpose of visualising the passage of time. Digital is great, but analogue will be with us for the foreseeable future (and I'm including in that the representation of analogue in a digital form, e.g. on smartwatches that provide a classic clock face graphic).

Phones from 2000-2010. Linux/PostmarketOS allows you to run these as mini webservers with webcam's built-in (depending on chip support)
Also PostmarketOS are looking for a new name, so if you've got a suggestion put it here: https://nextcloud.postmarketos.org/apps/forms/s/cAYZZrCqLnrfMPEMAAonCWwx

Your caveman brain. People think they're educated an enlightened and everything they do now is so well thought out. Nope, the caveman is in the driving seat for all of us. Even your most high level meetings and interviews are influenced by how hungry, horny, or hurt you are by a teasing comment yesterday. Everyone is looking to establish dominance at any cost, when you don't really need to.

Caring about your employees as if they were humans.
- Caring about other people in general really

Obligatory thought to cobol, which is stil the backbone of banking computers.
I would also think to the good old electromechanical relay which are still pretty common
More political, but whatever what imperator Musk thinks Privacy isn't obsolete
- Not only is it not obsolete, it's easier now than eight years ago when I started degoogling, there are so many decent alternatives nowadays to all kinds of services and apps.

I'd say vinyl. Looks like a thing from the 60s but it's still pretty relevant today
- I put vinyl siding on my house 15 years ago. Still looks brand new. Vinyl is here to stay.
- I want tot go one further and say music cassettes. Love their sound and way more compact than vinyl. Sadly, there's no good new hardware being made at the moment, although I really like my We Are Rewind player, it's far from HiFi.
  
  Nah, gotta got vinyl because cassettes deteriorate just sitting in their cases while vinyl stays pristine ... until you actually play it, anyway -- but if you want to store an audio recording for longevity, press a gold version of a vinyl album.

clapper. plug it in and its good to go. don't want to block it in to much though and muffle sound getting to it.