which software would i use on linux to capture video from disney plus for personal use?

Unless you have a specific constraint not mentioned in your post, it would probably just be a waste of time compared to just downloading an existing rip from a torrent site. Especially considering most stuff on Disney+ is fairly mainstream and should be easy to find.
Trying to rip from Disney rather than finding a source to download it would be more time-consuming and would likely end up with worse quality than what the various scene groups get out.
- Disney+ has a lot of foreign language dubs, which even for mainstream titles are exceedingly hard to find on torrent sites. It's the thing holding me back from getting a NAS and going full pirate.
  
  That's for sure one of the bigger constraints possible, and one I'm most familiar with as my first language isn't English. You can still usually find stuff though, although it might require private torrent trackers or Usenet.
  
  I always wondered about this. I have the same TV series as local MP4 files: one with English audio, and another with Greek. I thought I could just extract the audio tracks and use them to build an MKV file with multiple audio, but it always ended up with an audio sync error. One track would always be in sync at the beginning, but 20min in could be out of sync by as much as 5seconds.
  How do people build multi-audio files if the audio tracks aren't part of the original source?
  
  Private trackers have it.
- Disney+ has some TV shows for which there isnt good availability on Usenet or torrent. Mostly older kids shows.
  
  Really? Any examples offhand?
  
  I bet you could find what you’re looking for on Old Toons World.
- Not OP but the only problem with specifically Disney + is they have a TON of shorts that I never can find on any scraper/website

I guess OBS? Works on Windows if you use the webbrowser and disable Hardware Acceleration. Be advised though, the resolution and bitrate on browsers alone could be limited and also on linux clients.
I think the best way is still to rely on already ripped content. Though if you want to start creating webrips yourself, afaik people use their cookies and use the streams, that the browsers/applications get pushed and turn them into other video formats. But not at all a pro on this topic. Someone else here is surely better informed than me on this topic.

As everyone else is saying the issue is that priacy is easier.
That said if you have a HDMI recorder and a HDMI splitter (1 in 2 out) you can strip HDCP and record the signal.
With that said there are some fruity USB c tablets which will get you better results. Droid tablets can work too if you are OK with gui

If you don't want to spend any more:
VirtualBox
OBS
VirtualBox to get around DRM (recording software can be seen if video used in host system) and OBS will allow you to record a window.
If mkv is too large then you can use Handbrake to convert it to MP4 or m4v.
Just be sure to have any mics muted during recording and also mute notifications
- OBS supports capturing audio from a specific application, so if you set that up you don't need to be careful with foreign sounds.
  
  True, OBS sometimes makes windows have the same names so the VM program could have the same name as the running VM. Just something I did with my first time using it for that since I didn't know better.

Probably OBS would be your first try, it should be able to do a video capture and is Linux compatible.
Or if you're willing to set up a VM running Windows you could look into the non-free closed-source stream rippers for 720p/1080p. e.g. RedFox AnyStream, DVDFab StreamFab, etc.
EDIT: Just realized AnyStream also has Linux builds so that could be a non-free closed-source solution.
- Yea, OBS

I don't know if they implemented something against screen recording, but I use SimpleScreenRecorder. But even VLC can do screen recording using the "Stream" option.
- Lol, can they even?

If you screencap, use Firefox - you may get a blank screen if you attempt to capture Chrome
- Also disable hardware acceleration on your browser if the recording/streaming software only gets a black screen.

AnyStream?
I haven't used it, but it is available for Debian/Fedora, despite being proprietary.
And you have to pay for it.
- And you have to pay for it.
  This might be the first time these words have appeared in this configuration on this community.
- This seems to be the best option, since screen capture comes with many other issues.

I needed to capture my desktop a few days ago, Vokodscreen did it simply and worked like a charm