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Random Au headcanon time:
In TMNT 2012, Leo got a voice change due to the Shredder messing up his vocal cords after the Foot ambush. It's spawned a few headcanons that Leo can't speak for long periods of time because his voice would give out on him if he spoke too much or yelled too loud.
I can't remember where but I saw this one post that expanded on that idea with Leo having a love for singing and would often sing his brothers to sleep some nights. When Shredder damaged Leo's throat, he was devastated because he couldn't sing as well as he used too. His brothers on the other hand, loved his singing voice because it reminds them that Leo's still here and safe.
I want to add this headcanon to the Mutant Mashup Au. DaVinci would probably sing along with Niccolo when he did his funny voices. Vin might have gotten into singing once Nico showed him where he learned the countries of the world song.
I imagine that sometime after the Kraang Invasion, once everything settles down, the boys notice DaVinci is a lot quieter than he normally is. Once it finally clicks that Vin can't talk at the moment, Orange goes to Draxum for help. By this point Draxum is a reformed lad that casually accepts he's been forcibly adopted and goes to help DaVinci.
Whether through some sort of mystic healing spell (similar to 2012's Healing Hands technique) or actual surgery, DaVinci is able to speak again without much pain. There are times when his throat flares up but those moments only come after prolonged use of his voice. DaVinci is a pretty quiet kid when compared to his family so that thankfully doesn't happen much.
Just a little thing, DaVinci probably felt proud of his voice and must've felt so insecure about singing after his throat got better. To the point where the rest of the boys, even April, May and Casey, got worried he stopped singing altogether. Blue especially worried because he hates when anyone in his family is hurting, that's part of why he's the medic. It takes a while but the family eventually convince DaVinci that they'll love whatever his new voice sounds like no matter what.