My next suggestion is really very basic, but we can’t be sure if we don’t check.

Open Avast (from start menu for example) and from the main GUI go to

Settings

→ basic → appearance → “Show avast! tray icon”. Is that checkbox checked?

→ Status Bar → check all.
→ Troubleshooting → “enable avast! self defense module” “must” be checked.

If you need to make changes to those settings to match them as requested, please save the settings, and reboot and review that they are still the same as you saved them.

Please report back.