Selfhosted

Shoko + shokofin is a great solution for anime, but if you get most of your stuff from streaming sources you might have to manually link almost everything (or add it to AniDB). I could be wrong and it wouldn't hurt to check first with some of your catalogue. You could even just log into AniDB and look at the releases for an anime you have, maybe compare file hashes or test it with shoko desktop if that still exists.

Even when set up "correctly" there are going to be a few shows where things are wrong, just due to different groups classifying series differently in some cases.

for the basics, you just need to ensure you have the right folder structure and the standard episode numbering in the filename, usually "/libraryroot/Show Title/Season 01/Show title - Episode Name - S01E01.file"

there are cases where a show has multiple seasons but some are classified as a separate show, some are separate single cour seasons, some are multiple cour seasons, specials etc. and that changes based on where you get your metadata and often differs from what the release groups will use.

So to tidy it up in those situations I use TinyMediaManager to manually build the metadata and write that to a file that jellyfin will use above all other providers.

I've only needed to do that in full detail for Monogatari series though, since I have my preferred way to arrange that abominable mess. pretty much everything else I stick with whatever the AniDB plugin wants and adjust my files to suit.

For my jellyfin a proper directory structure seems to be good enough most of the time:

series name/Season 01/S01E01.mp4

https://jellyfin.org/docs/general/server/media/shows/

1. Follow the Trash Guides exactly for your arr stack setup. Don’t try to get fancy or take a shortcut. If you’ve already set up something differently, just redo it. Better to spend a little time now than a lot later.
2. Set up Tailscale. The free tier is probably fine for you, but if you’re extra paranoid you can run your own Headscale server instead.
3. Take notes. What you set up, what your docker files and configs are, and add any troubleshooting info as it comes up.
4. Use a password manager and keep everything in it.

I like using sonarr(https://sonarr.tv/) - you can assign the episodes and seasons. Then you can have it rename them. There is an absolute episode numbering setting. Trash guides is helpful too: https://trash-guides.info/

My setup is for Plex, but I'm assuming Jellyfin should be able to consume the library names the same

While it is a bit of work to rename the files that would still be my recommendation. I find jellyfin to be a great match for my anime that way.

Like others mentioned file structure is the most important. In addition you can also grab the AniDB plugin and set it as the primary metadata source in Jellyfin. (I had it for quite a while so dunno how much difference it makes compared to TVDB, but from experience I practically never had wrong metadata on an anime)

TinyMediaManager renames all my files (anime or otherwise) so that any service can work with them. There's very rarely anything that isn't recognised properly.

Proper directory sorting and manual meta data hint entry is literally the number one way to make jellyfin behave properly. If you're on linux kRename (available on flathub) makes this relatively painless.

Series (premiere year) [imdb or other db id]/
                             Season ##/
                                   Series Name - S##E## - Epsiode Title.ext

Works 99.9% of the time. As long as you have either the imdb id (mostly normie anime will be fine with this) or an anidb plugin or similar for the obscure stuff it'll work 100% of the time.

This also allows easy searching of individual episodes outside of jellyfin, should you find an episode that somehow got corrupted or otherwise is just not what it should be.

Bonus: If you take the time to do this (literally 8-10 hours max for a collection of tens of thousands of episodes of shows) your library becomes much more portable as any competitor to jellyfin and any addons will now just automagically detect everything properly.

I have never had an issue with properly named files.

Some tools to help with bulk renaming.

Krename

Link - https://github.com/KDE/krename

Useful for bulk renaming uniform files. I often use it to add the season when the file names just have the episode number.

Filebot

Link - https://www.filebot.net/

Great for renaming messy files. You can match the show name then it will try to get the season, episode and episode name

MediaElch

Link - https://mediaelch.github.io/mediaelch-doc/index.html

Excellent for pulling the metadata for a show into local nfo files.

Once you have the show name, season and episode number you can scrape TVDB or other sites for the episode data, thumbnails, actors, posters, etc

I then have Jellyfin use the local metadata that MediaElch has created.