What is it for, tag called "TaggedPDF" ?
It has a value "Yes", what does it mean?
Does it mean that PDF file has some (hidden) tags, that I've removed using ExifTool?
I have no idea what that tag is used for but exiftool will display any tags it knows about.
But as it says on the PDF tags page (https://exiftool.org/TagNames/PDF.html), any edits exiftool makes to a pdf file are reversible due to the way exiftool writes pdf data. In order to permanently remove the data, the file needs to be linearized, as per the instruction on that page.
I did find this page (https://www.grapecity.com/documents-api-pdf/docs/online/taggedpdf.html) in regards to what a tagged pdf is.