based on lwaxana in tng interacting with deanna, i think it's safe to infer that betazoids when talking to each other use only their telepathy and that this is more standard practice. which makes sense but it does begs the question of: why can betazoids even speak with their mouths?
like. it seems that telepathy is better and preferred, so verbal language should not be developing at the same speeds as the not telepathic species. humans have a complicated and vast language because it's all we have - but if you could just drop the idea if something into soneone's head, why bother naming it?
and obviously when we see telepathy communication on screen, it's shown as people hearing verbal language without the use of their ears. but if you really think abt it, then verbal language would be secondary to an all-telepathic society. thinking phonetics at each other makes little sense, most probably the process is more like sending each other ideas or impressions. it's also possible that BML (betazoid mind language) is being translated by the UT into sounds and this what we see.
anyway, here are some of my headcanons/theories:
1. betazoids don't have a native verbal language, at all. lwaxana speaks federation standard to deanna, or deanna's UT picks up the mind language.
since lwaxana is an ambassador it would make more sense for her to know several languages. but an average betazoid that doesn't come in contact with other cultures doesn't know how to speak with their mouths. it would be interesting to theorize if they would still sing, since the development of music is so closely tied to language. similarly, it would be interesting in this case to see what their writing system looks like.
2. there is a subset of betazoids that can't read minds, like deanna, and has always historically been present, and they use BVL (betazoid verbal language) like Deaf people on earth use various sign languages. (but by following star trek logic all planets have united into one state, so there is only one BVL). perhaps this language was taught in schools before first contact to accomodate that minority, or that minority is big enough that every family had at least BVL speaker. after first contact this language was adapted into use with other civilizations
3.1 betazoids do have speech and use it commonly, maybe for cultural or ceremonial reasons. maybe speech is older than the telepathic sense evolving somehow and was kept in use for tradition or communication in certain conditions (like over big distances).
3.2 betazoids had their first contact a very long time ago, or they're not the only species living on betazed. so the BVL did evolve to communicate with non-betazoids, but it didn't have to be adapted in recent history, it just naturally is a part of every betazoid's toolbox by now.
either way, i think it would be interesting to see a betazoid character that only communicated with telepathy come into contant with a species they cannot speak to (maybe for politeness reasons, or that species is all completely immune to mind reading and mind-speaking) and struggle to adapt to verbal communication. they would probably struggle to choose words and express thought in this form.
if they only used BVL/Federarion Standard/Any Speaking very sparingly before and started in adulthood then their muscles would probably be not well developed enough and they would have a speech impediment. actually it's interesting to think abt how the UT would translate someone who isn't speaking their language "correctly"...
technically, could you put your specific impeded speech as a "language" and have it come out as the "standard" version? it could be an accesibility tool then. on the other hand, if the UT couldn't handle your own non-standard input and wouldn't translate you, that'd suck - this is a common problem (also with certain accents) with modern speech to text & voice command technology, but it seems like it's not a problem in trek that we see.