Illustrator v26.1
Windows 10 Enterprise

When opening an illustrator file created under a previous version of illustrator that was saved and/or created without a color profile assigned (not color managed), with color settings set to inform/warn the user of the missing profile, assigning the profile at file open when the prompt is displayed or clicking OK with "leave as is (don't color manage)" selected and then selecting edit > assign profile and assigning a color profile...

then saving the document with ctrl+s or File > save does not save the file with the assigned color profile. Opening the file again presents the same missing color profile prompt.

Assigning the color profile via the prompt or via edit menu and then using File > Save As and overwriting (or saving a new version with a different filename) saves the assigned color profile correctly.