You are correct that the web site ( https://www.dvdfab.cn/apple-tv-plus-downloader-en1.htm?trackid=headmenu2,downloadpage ) advertises 1080p for apple.
And you are correct, its not currently downloading as 1080p from AppleTV+
Since originally being made available, the AppleTV+ module was downloading by "watching" at 1x, and the video download was 1080p video and 2 channel audio. With version 4.0.0.7 StreamFab changed the AppleTV+ module to allow for faster downloads (i.e. download without having to watch at 1x). The change in download process for other services to this faster method had usually meant 720p video BUT increase to 5.1 audio.
Prior to 4.0.0.7 when I downloaded Greyhound (at 1x while "watching") it was 1080p. However starting with 4.0.0.7 I've downloaded Greyhound and a few other movies and shows such as Ted Lasso several times and ended up odd resolutions like 1186x496 and 1224x512, which PLEX identifies as 576P, even the video bit rates are much lower, and audio is still 2 channel AAC.
For more info and discussion, see -> https://forum.dvdfab.cn/forum/software-support-english/youtube-to-mp3-youtube-video-downloader/397738-4-0-0-7-apple-tv-new-way I have a few posts in there with details of the files downloaded with 4.0.0.6 and lower, and now.
HBO Max, Netflix, Paramount+ are still up to 1080p with up to 5.1 audio, although I have had a handful older titles come down as "576p" from Netflix.
As you mention yes, Disney+ and Hulu are max 720p downloads. And Amazon we are still waiting to get back to better than SD quality.