The thing that I miss the most on iOS (don't know if this is the case with Android as well) is for the OS and apps to just remember which language I last used when communicating with a given person. Just because I recently wrote a message to my Danish girlfriend doesn't mean I want the Danish keyboard instead of the English one when I go to write a message to my Canadian friend. Seriously, is nobody at Apple bilingual? How they've managed to release 11 versions of iOS and never implemented something as simple and useful as this is beyond me...
Honestly I'd probably be fine with a combined Swedish & English keyboard for most of my daily interactions (also Swede's in general and in the tech sector in particular mix in a lot of english).
However being half dane close to the german border and with a interest in language I do occasionally use other languages as well which results in me having 6 more active keyboards, and while I mostly toggle between Swedish, English and some occasional emoji it's quite a hassle to shift though half a dozen keyboards every other time.
Interested to hear what solution would be better for you. I live in Sweden and while I don’t speak Swedish everyone I work with basically does as you describe, the keyboard toggle between English/Swedish keyboards.
Frankly because I work with Danes and Swedes all the time it’s usually enough to hold down A and O when I need to type å, ö, ø, etc. but I usually don’t type in those languages. It’s mostly for locations and the occasional translation.
Why not do like I do with English, Swedish and Portuguese: use the English keyboard and long press the letters you need to type that have a diacritic, like: é, à, á, ê, õ, ... in Portuguese or å, ö, ä in Swedish?
This saves me the hassle of switching keyboards all the time, I just learned what long presses I need to use in the US International keyboard and can type even in German :)
I know that it is not what you are asking for, but I believe Facebook messenger indeed does this. So it is certainly not a technical limitation but purely a lacking implementation.