"Prayer language” and “speaking in tongues” - to some people - are two very different things. I go to a charismatic church down in Florida almost every year to do a concert. There, speaking in tongues was explained to me as God speaking through a person in a heavenly language that then needs, and must have, interpretation into human language by someone with that gift. I’ve witnessed this. Someone interrupts a service speaking in tongues. The pastor stops speaking, steps back, looks down and lets the tongue speaker finish. Then, he asks if anyone present has an interpretation. Someone stands up and says they do. The pastor steps back again. The interpreter begins to interpret. My wife saw this happen three times in one service at the Brooklyn Tabernacle - the message spoken in tongues was translated as all scripture that pertained to the sermon beautifully and there was no distraction for those used to tongue speaking in the services, the speaker wasn’t exalted above everyone else as a superior Christian, and it seemed to serve a purpose.
Prayer language has been explained to me as spontaneous speaking to God in a “soul language.” The verse about the Spirit knowing every groan in the human heart is used to back this sometimes. Our heart, presumably, groans in an unknown language to God on our behalf and God understands it. It’s not used to speak to others but is a private communication tool for speaking to God what we cannot find words to say.
Then there’s Pentecost. At Pentecost the ability to speak in human languages previously unlearned was given (me speaking French for example). OR the ability for the people from many nations to hear one man’s speech in their own language (me speaking English but a French guy hearing French and a German guy hearing German etc.) was given. There’s a little debate on what exactly happened at Pentecost. The point of the gift though, whatever it was, at Pentecost, does seem to be communicating a message about God to many people from many earthly language groups all at once.
I do believe speaking in tongues happened at Pentecost. I think that COULD happen today only because the bible doesn’t say explicitly that it couldn’t - not that I’ve seen.
I think it’s also possible for God to speak through humans today if He chooses but Paul is clear that there must be an interpreter present when that happens and if there is none the tongue speaker must stay silent, which means he/she has control over the gift. It’s not possession. I question the authenticity of tongues when order isn’t kept and when the interpretation is “new revelation” or contradicts what God has already revealed of Himself through scripture.
I don’t know about prayer language but I don’t believe the verses I’ve been shown to support it are legitimate backing. It might exist. I’m not telling God what He can’t do. It certainly doesn’t contradict anything I know of Him but I don’t see it mentioned in scripture either so I just don’t know.