I think a simplest solution might be that illustrator stores the name of font which was converted to outlines as metadata. So when hovering mouse over outlined text the font name cane be shown as popup or somewhere in panels. That way all the guesswork to identify exact font can be avoided. If its not possible to keep link of outlined text to font name, those font names can be stored for the whole document and shown somewhere in a panel as "Fonts used".

I think first step and easiest, that while outlining text Illustrator should keep the text information somewhere, to then switch back or even for information only.

Once a design has been created, and you have outlined the text without saving an editable version, you would click on the outlined text and ask Illustrator to detect what font is being used. This would apply to fonts you have installed, and Adobe Fonts available to you.

Related to
Convert outline text to editable text
https://illustrator.uservoice.com/forums/333657/suggestions/33183166

This would be great for designs with no style guide where the text has been expanded or converted to outlines.

We could group the letter shapes or select all of them and [Right Click] > Identify font. Illustrator would then compare the shapes to a font database, Google fonts, etc. to provide a list of the most similar fonts, or the "exact match" if it knows for sure.

I was thinking if I had a tool to pull a color out of a ready picture.
Why don't I have a tool to pull the font type out of a ready-made image?
Like if i see a nice font type in a photo or post or etc
And i want to use it in my work but i don't know the name of it
I need i tool the help me pick up the type of font

Yeah, some collaboration with WhatTheFont or WhatFontIs could be useful.
Meanwhile you can you their app or website.

Select outlined type or a photo of a typeface (rasterized type and the app matches it to the nearest similar font in the library. It could offer several options but it will never say "sorry no similar font found." You could even draw a character and it would find the closest font to it.

This is valuable to anyone in production who is asked to make changes to outlined or rasterized type or when the client doesn't provide the font name (which they never do) or the client says "can you use Buscemi Bold and you don't have it. it will find something close enough. I worked in an art department where we spent several hours per week trying to match fonts. This feature would have saved a lot of time.

When converting customer-supplied logos into vector artwork I often need to match their fonts (sometimes easier than others). I use the website WhatTheFont which does a good job, a feature like this would be very useful within illustrator. Select the area of an image click "find font" and illustrator suggests what it thinks are the correct fonts, either within your own font list, Adobe Fonts or other external websites.

This is a great idea!