I then tried various sorts of C-h and websearch, without success.
Please check the manual first! (or second, after docstrings) (eshell) Dollars Expansion:
Eshell has different ‘$’ expansion syntax from other shells. There are
some similarities, but don’t let these lull you into a false sense of
Returns the output of ‘...
The quoted limitation does not exist any longer. Moreover, the function tramp-adb-handle-shell-command does not exist any longer. All different implementations of shell-command in Tramp have been unified in tramp-handle-shell-command, which is able to run several asynchronous processes in parallel.
This is brand-new, it will appear with Tramp 2.4.2 (planned ...