[booth] `pcs booth sync` is a misnomer, carries semantics of what would be expected with imaginary `pcs booth push`

With _synchronization_, at least a weak notion of intelligence or
carefulness is expected (naturally absorbing user's worries).

Therefore it is rather inappropriate for `sync` to mean "enforce
my local version". That's not a synchronization, it's a _dictate_
that should rather labelled as `push`, as is customary in the field.

Start by locating the `pcs booth sync` command and its user-facing documentation. Compare the command's current behavior with the issue's distinction between synchronization and enforcing a local version, then identify the affected CLI and documentation scope. Done requires an agreed design for the command names and semantics; the issue does not name specific files or tests.

Written by the indexing model from the issue text.