Well, unfotunately, I'd say your findings are accurate - yess the camera reports the AF/MF setting and DPP picks up on it, but Photoshop (and Lightroom) do not.
There are other settings that may not get picked up by Potoshop as well. A lot of this is because Canon stores and encodes some of its Exi/Metadata into a "Maker's Notes" section and this data is "not shared" with other exif readers/Ra processors. But, I don't have the technical details about that. And, it is not necessarily consistent. For example, the in-Camera Picture Styles are stored in a file even for a Raw file, and so when DPP opens a Raw file it "reads" the Picture Style (and related settings) and applies all that to the Raw preview and default conversion.
But Lightroom/Photoshop do not read those Picture Styles -- Canon doesn't share with Adobe and Adobe either hasn't had the time/resources to decode every Picture Style for every camera they support or it's just not worth the R&D.
And then, on the other hand, the camera saves some kind of information for White Balance, and Adobe has done the work to do a reasonable job of decoding that -- if you set different WB presets in the camera the images will show up in Lightoom with a different WB applied.
So, it can be inconsistent, but it's there. Some stuff Canon puts in the "straight Exif" and it is easily read but some stuff it stores things in that "other place" and evidently encodes it. But I'm just saying some very general things here because I really don't know the technical "stuff" behind it all.