Background: I bought a Blue-ray set that came with a code for the digital copy. This was back before Funimation was acquired. I could go through and rip my discs since Sony seems to be on the verge of nuking my digital copies, but teaching myself yt-dlp seemed more convenient.

Here's are the settings I ended up using with yt-dlp to download digital copies from Funimation. I paste all three of these at the same time into the terminal, but you can paste them one at a time if you want. I'm on Linux and log into Funimation with Firefox, but it should be almost the same for Windows. The URL needs to be changed for each download. I have noticed some downloads stalling, but I if I refresh the pages that lists the episodes, the download resumes.

yt-dlp --cookies-from-browser firefox -F https://www.funimation.com/path-to-episode
yt-dlp --cookies-from-browser firefox --list-subs https://www.funimation.com/path-to-episode
yt-dlp --cookies-from-browser firefox --write-description --write-info-json --write-sub --write-thumbnail --embed-subs -o '~/Path/To/Downloads/Video/Folder/s%(season_number)02de%(episode_number)02d - %(title)s.%(ext)s' https://www.funimation.com/path-to-episode

Here's what each part means:

Line 1:

 -F

Outputs you which versions are available. I have it tell me this, so I can make sure when I run Line 3 the output matches the highest quality listed in the output from Line 1

 --cookies-from-browser firefox

Tells yt-dlp to use the cookies from your browser to authenicate the download since it's only available if you're logged in.

Line 2:

 --list-subs

Tells yt-dlp to list the kinds of subtitles it can find. I have a few episodes that it cannot find any subtitles even though they're avaiable when streaming. It seems like it's something weird with some episodes, and is probably related to this: https://github.com/yt-dlp/yt-dlp/issues/1656

Line 3:

 --write-description

Makes a .description text file with the description metadata in it in the same folder you download to.

 --write-info-json

Makes an .info.json json/text file with all the metadata in it in the same folder you download to.

 --write-sub

Makes an .srt srt/text file with the subtitles in it in the same folder you download to.

 --write-thumbnail

Makes a .jpg image file of the thumbnail artwork for the episode in the same folder you download to.

 --embed-subs

Embeds the subtitles in the downloaded video file.

 -o '~/Path/To/Downloads/Video/Folder/s%(season_number)02de%(episode_number)02d - %(title)s.%(ext)s'

Specifies the download path, and formats the filename as: s##e## - Episode Title.mp4

Hope this helps someone. I realize you could skip all this hassle and just pirate it somewhere, but I'm not sure where to find this specific release other than the digital copy on Funimation.