PSD saves color profile in "untagged" file, Bridge shows as embedded...
I was trying to track down a situation where Bridge was previewing files different than how Photoshop was viewing them and noticed that PSD saves color profile in the metadata of "untagged" PSD files. Bridge then shows the files as having embedded profiles. Saving image in other format for example JPG removes the data that Bridge seems to be accessing. I've cleared the Bridge cache.
metadata from PSD file of image with profile removed via Edit/Assign Profile/Don't color manage :
ad47d4ecb02f</stRef:originalDocumentID>
</xmpMM:DerivedFrom>
<xmp:ModifyDate>2018-09-20T07:58:29-04:00</xmp:ModifyDate>
<xmp:CreatorTool>Adobe Photoshop CC 2018 (Macintosh)</xmp:CreatorTool>
<xmp:CreateDate>2003-05-05T09:26:13-04:00</xmp:CreateDate>
<xmp:MetadataDate>2018-09-20T07:58:29-04:00</xmp:MetadataDate>
<dc:format>application/vnd.adobe.photoshop</dc:format>
<photoshop:ColorMode>3</photoshop:ColorMode>
<photoshop:ICCProfile>Adobe RGB (1998)</photoshop:ICCProfile>
<photoshop:TextLayers>
<rdf:Bag>
<rdf:li rdf:parseType="Resource">
Photoshop image on left showing "untagged", Bridge preview on right:

