Do you know of a DRM-free music app with an algorithm?

DIY music libraries are you only option.
- I don't want to maintain my own library of music, which is why I use streaming services.
  I also said I'd like to have an algorithm.
  
  I converted my MP3 collection to files on my PC last summer, after getting sick of Spotify's price increases. If you manage to find a DRM-Free music app I'd love to hear about it, but I'm confident none exist.
  When I want to try something new I log on to Spotify's web player using Brave browser (because it blocks ads and tracking), sample the stuff the app curated for me, and then use a Youtube-to-MP3 converter to download the files.
  Sorry, I know that's not the kind of info you're looking for. I'm just pretty sure what you're asking for isn't a thing.

Instead of "with an algorithm" say "with a recommendation algorithm". Algorithm is a very generic term that can mean anything.
- What else could it mean in terms of a music app?
  
  Sorting algorithms, categorization algorithms, compression algorithms, etc.

How would you define a DRM-free online service? If you aren't managing your own files, why would DRM free matter?
- Personally, I’d like an open API so I could use it with foobar2000. Not OP but I long for the same thing. I’ve done it, and managing, storing, backing up, my music library costs more than Spotify. And assuming you don’t just pirate everything, add the cost of purchasing albums on top of that. And my time is worth minimum wage at least. I would happily pay someone to just handle this stuff.
- Personally, I’d like an open API so I could use it with foobar2000. Not OP but I long for the same thing. I’ve done it, and managing, storing, backing up, my music library costs more than Spotify. And assuming you don’t just pirate everything, add the cost of purchasing albums on top of that. And my time is worth minimum wage at least. I would happily pay someone to just handle this stuff.
- Personally, I’d like an open API so I could use it with foobar2000. Not OP but I long for the same thing. I’ve done it, and managing, storing, backing up, my music library costs more than Spotify. And assuming you don’t just pirate everything, add the cost of purchasing albums on top of that. And my time is worth minimum wage at least. I would happily pay someone to just handle this stuff.
- Personally, I’d like an open API so I could use it with foobar2000. Not OP but I long for the same thing. I’ve done it, and managing, storing, backing up, my music library costs more than Spotify. And assuming you don’t just pirate everything, add the cost of purchasing albums on top of that. And my time is worth minimum wage at least. I would happily pay someone to just handle this stuff.
- Out of principle.
  
  I mean I understand and support DRM free media, but I literally don't understand what OP is asking for. If they don't want to own/manage the music, then what part would be DRM free?

Bandcamp.com
You can listen to the tracks, ad-free, get recommendations below the album listing (maybe other ways too), buy DRM-free and support the artists better than any streaming service would be willing to.
If you do go local library and are looking for recommendation algorithm, Apple Music (the app, not the streaming service) sells DRM-free as well and has the Genius function that will group songs based on similar preferences. However, I don’t believe it will pull in recommendations outside your own library. Worth checking.

If you don't want to maintain your own library why does it matter whether it has DRM?
- I don't want to support services intentionally restricting users. It's defective by design

I scrobble to Last.fm for recommendations, but I'm not sure you can get DRM free without maintaining your own library.
- I think I'll have to keep using ytm
  
  I believe you could use listenbrainz to get a bit of an algorythmic recommendation feed. It can connect with your jellyfin (and probably plex) and subscriptions like apple music and soundcloud and get recommendatiom.
  But listening to that is probably via cloud services.

This isn't exactly what you asked for, but I want to recommend somafm, which is an internet radio site. They have a bunch of different channels with different themes/styles.
This is a good option since you don't want to maintain a library. Rather than a recommendation algorithm, the channels are intentionally curated by people, and occasionally live dj-ed.
You can use their web player, but they also provide stream links for any media player that can handle them. VLC can do that, or you can use a mobile app.
- Thanks for the suggestion! Will give it a try tomorrow.

You can do what I do, and use an app with an algorithm, then find those songs elsewhere through a service of choice. I personally use Deezer for discovery, then buy on Qobuz. From there, I can just use Qobuz, or move the files elsewhere.
Apple Music/iTunes is the only thing somewhat close, and was my old preference. iTunes DRM is practically non-existent, and Apple Music syncs with iTunes purchases (even if a song is on iTunes only), with an algorithm on top.

Sorry if I sound dense but when you say non drm what do you mean?
I have used Apple Music for years and not had any issues.
- It stands for digital rights management. Apple Music has drm. I do recall back in the day that anything purchased on iTunes was pretty easy to strip the drm off of, but I don’t think that’s the case anymore.
  
  I've moved songs to local storage from iTunes in recent memory. It's literally just easily convertible files that all of my software and hardware can already play. Of course Apple Music is DRM, though, it's streaming.
- It's defective by design

Deezer maybe? Qobuz?

Spotify has DRM, but it's relatively easy to bypass with something like librespot if you want to download tracks.
- Tried (I believe) zotify to download the tracks directly as m4a files.
  Luckily I have a family plan so I can generate throwaway accounts.

Maybe iTunes? I haven't used it, don't know if it has algorithms.