Yes, Exiftool does support those tags, but they must be written to the file for exiftool to be able to read them. The issue is that these tags are not written to the file by Bridge, but are included in the 'Raw Data' view of the XMP, which makes it look like they have been written to the file.
Since those tags are used internally by Bridge, and not actually written to the file, exiftool cannot extract the data from the nonexistent tags.
There is a lot of data that is held in the metadata for various reasons, you can even add your very own.
The tags you mentioned are used by Photoshop and various other applications so they can get the mode, profile of the document.
The issue is that the Bridge File Info panel is showing these tags in the XMP for the image, but if you check the XMP of the file, those tags aren't there.
As a side issue, Bridge File Info panel is also showing the XMP in a different structure to that which exists in the actual file. There are two issues here really
- ACR is not writing the photoshop:ColorMode tag (or the photoshop:ICCProfile tag) to the JPEG (I checked the .xmp sidecar file for the RAW file and the photoshop:ColorMode tag does exist in there, but does not exist in the JPEG file converted through ACR).
- Bridge's File Info panel is showing data in the XMP that is not actually there.
Although I would like the ColorMode tag added to the image, I don't think point 1 is a real issue, since the ICC profile is embedded okay. Point 2 does appear to be a bug (or at least it is confusing if it is intended behaviour).