But pv(1) is just blindly attempting to emit "\r[progress bar ASCII-art]\n" (plus a few regular lines) to stderr every second; and interleaving that into your PTY buffer along with actual lines of stderr output from your producer command, will just result in mush — a barrage of new progress bars on new lines, overwriting any lines emitted directly before them.
Having two things both writing to stderr, where one's trying to do something TUI-ish, and the other is attempting to write regular text lines, is the problem statement of 3, not the solution to it.
A solution, AFAICT, would look more like: enabling pv(1) to (somehow) capture the stderr of the entire command-line, and manage it, along with drawing the progress bar. Probably by splitting pv(1) into two programs — one that goes inside the command-line, watches progress, and emits progress logs as specially-tagged little messages (think: the UUID-like heredoc tags used in MIME-email binary-embeds) without any ANSI escape codes; and another, which wraps your whole command line, parsing out the messages emitted by the inner pv(1) to render a progress bar on the top/bottom of the PTY buffer, while streaming the regular lines across the rest of the PTY buffer. (Probably all on the PTY secondary buffer, like less(1) or a text editor.)
Another, probably simpler, solution would be to have a flag that tells pv(1) to log progress "events" (as JSON or whatever) to a named-FIFO filepath it would create (and then delete when the pipeline is over) — or to a loopback-interface TCP port it would listen on — and otherwise be silent; and then to have another command you can run asynchronously to your command-line, to open that named FIFO/connect to that port, and consume the events from it, rendering them as a progress bar; which would also quit when the FIFO gets deleted / when the socket is closed by the remote. Then you could run that command, instead of watch(2), in another tmux(2) pane, or wherever you like.
