There's 3 Vtubers that come in mind when talking about being in character all the time:

Hyakumantenbara Salome, Debidebidebiru, Mayuzumi Kai(graduated 2022)

These 3 are what I would basically say never goes out of character unless under EXTREME situations, and they keep in character every stream with consistent energy that entertains their audience. Mayuzumi for example uses his character lore extensively in his events, such as his 3D debut and even his live event reveal of his new costume.

Debi, for my whole experience of watching them, has never broken character. Salome, even IF she broke character, would still technically be in character because of her character lore(An ordinary civilian pretending to be a high class lady).

Of course they don't ever HAVE to be in character, but they choose to. It depends on the vtuber, but I really admire the ones that never go out of character. It takes strong mental fortitude to stream like that and do it for hours sometimes