Hey MPU,
I have been trying to figure this out and I can’t wrap my brain around it. I am taking an Intro to Greek Class this semester. I added Greek via System Preferences > Language & Region > Keyboard. I also have the box checked for “Show input menu in menu bar”…There’s no flag in my menu bar!!! I quit Bartender in case there was something there missing, but that didn’t help. Any other suggestions?
I have never done something like that but I just tried to add the Greek keyboard to my system (MacOS Catalina, German system) and the German flag immediately showed up in the menu bar. Then I was able to change it to Greek.
Unfortunately, I was not able to type with Greek letters on my German keyboard… That might be an issue I have caused because of using CleanMyMac (removing language files from the system that are “not necessary”), I am not sure about that, though.
My Bartender settings for Text Input are: Menu bar item should: Show.
Maybe someone else has an idea what is going on…
Finally got it figured out and I am not sure how this happened.
These 3 items were using the same keyboard shortcut
I reset all 3 to their originals. I re-added the keyboards and checked the input menu box.
I restarted my mac and now I can see the flag(s) again. 
I hate it when that happens - and that has happened to me before, too (not with Spotlight, but with 1Password and Keyboard Maestro). 
Good to hear that you were able to figure it out! Stuff like that is not easy to find…