tmux bell-action vs monitor-activity for silent background job alerts

Goal

Configure tmux to notify a user when a long‑running background process finishes, but without audible beeps or excessive status‑bar flashing.

Constraints

• System sound manager may mute the terminal bell.
• Frequent output from background jobs can cause visual clutter if monitor-activity is enabled.
• The solution must work across common terminal emulators (xterm, iTerm2, GNOME Terminal).

Uncertainty

The interaction between bell-action values (e.g., alert, screen) and terminal/OS sound settings is not fully documented, and it is unclear whether monitor-activity can be tuned to avoid noise while still providing a visual cue.

Questions

1. When the system bell is muted at the OS level, does setting bell-action to alert still trigger a visual flash in tmux?
2. Can monitor-activity be configured to ignore trivial output bursts (e.g., printf "\n") while still highlighting when a background job emits a completion message?
3. Is there a recommended combination of bell-action and monitor-activity that provides a silent, non‑intrusive alert across all major terminal emulators?