I’m not exactly certain from your description how your field is configured, but you would probably use a nested IF() statement along the lines of
IF(AND({CompletionDate}=BLANK(),{StartDate}=BLANK()),'No assigned dates',
IF({CompletionDate}=BLANK(),'No completion date',
IF({StartDate}=BLANK(),'No start date',
IF(IS_AFTER(TODAY(),{CompletionDate}),'Project late',
'Project on schedule'))))
As @Hashim_Warren notes, under the Pro plan you can use conditional colors, but that color tag applies to the entire record, not just the field. To flag the field directly, as @Elias_Gomez_Sainz mentioned, you can use emojis. For instance, in my Wardrobe Manager base, I report an unflagged date when the completion date is at least two days out, a date flagged with the Large Orange Diamond emoji if the completion date is today or tomorrow, and a date flagged with the Fire emoji if the completion date has passed. Here’s a snippet from the Wardrobe Manager Users Guide to demonstrate.
You can also use emojis and conditional colors together. (Please note the latter are defined per-view, while the former — being assigned at the field level — are visible in all views displaying that field. Also note that some OS/browser/font combinations may not display emoji in color — or at all.)
If you want dates to align nicely in views, you will need to left-pad your unflagged date with an en- or em-space character to match the indentation (unfortunately not shown in the above extract). I had to experiment with various combinations of fixed spaces and the space character to find one that matched.
