Just a thought, since those icons are similar to/same as in File Explorer maybe it's just Microsoft's way of tying everything together so maybe it will take some customization to change those, perhaps a third-party software.
You can add emojis to the start of the folder name instead. John [z3r010] suggested this to me about three years ago and I haven't found anything better. The method works in Firefox & Edge. I know nothing about Chrome.
Right-click on a Bookmarks Bar / Favourites Bar folder name & select Rename / Edit folder,
then move your cursor to the start of the folder name,
then press WinKey ;
then select the smiley face icon in the top left,
then look through the sets of available emojis [the various sets are selected using the icons at the bottom of the emoji panel],
and choose whatever you want.
I appreciate that this is not ideal. IE was much better in this regard.