I like how minicomputer used to mean "computer that's only as big as a chest freezer." Every now and then I hear laypeople use the term "mini-computer" to mean a computer that's really small by their standards, like a raspberry Pi.
In Swedish, the term "stordator", literally "big computer" refers to a mainframe.
I really like your idea of nano and picocomputers. It's consistent, and really reflects on the miniaturisation that we have seen since since the invention of the computer.
Since "computer" pre-dates digital, it might be a good time to come up with a more apt base term too. It's not as if most people's usage of them (at least as far as they know!) is performing arithmetic.
I suspect in the future we'll have curious historians trying to figure out how the phrase "personal computer" ended up being shortened to "phone".
[1] https://en.m.wikipedia.org/wiki/Portable_computer