..message icon in mac dock shows Red (1) unread message..
While no unread messages exist, these that appear in the Messages submenu from Dock icon have never been seen by me; nor opened on any Mac or iDevice.
Mac mini Late 2012 quad-core 2.3GHz server & dual stock 1-TB rotational
5400-RPM HDDs with two present macOS installs, that can boot this Mac.
An original Mavericks server edition (runs) shipped with this unit; was upgraded through El Capitan, then settled on primarily High Sierra. A Mojave installer, is on second HDD in a partition; didn't have time offline to delve into this. Too busy with life and estate issues, when mom passed.
I've been able to make the 'Red number' dot disappear, from my Mac's Messages dock icon, on occasion. Sometimes by restarting Mac into one of the Recovery modes (several installed macOS are accessible in partitioned hard drives) and use recovery offline. Start up into Opt and choose.. I've used the SMC Reset instructions for Mac desktop computers, with 5 steps.
This sometimes works; while Safe Boot sometimes does. Keys, dexterity
and timing; when exactly co-ordinated, deploy these startup options OK.
Or when I occasionally restart the Mac, this (1) unread message will just disappear. This past five months, this symptom has repeated; so the underlying cause remains. So guess I need make sure my 2FA logins are correct, erase and restore from backup, and try try again(?)
Had hoped to time this effort for when I haven't a dogpile of things using web browsers or webmail logins in use. I don't use Apple Mail, while login to browsers; and reply on Firefox ESR115.8; and/or Brave browser, version for High Sierra 10.13.6 Version 1.57.64 Chromium: 116.0.5845.188 (Official Build) (x86_64), and set 'Profile1' or 'Profile2' for best security.
This may or not be useful. While my iPhone is first edition SE-1 near end of its rope, w/ iOS 15.8.3. Hoped for last round number update, could happen.
A newer iPhone8+ awaits; needs new battery and iOS16.x While SE-1 runs a two+ y/o Apple battery, from authorized AK Mac local service provider. And harder to extract the SIM card; from durable LifeProof case.
Anyway, that's a longer story of some
associated factoids shaken into a pile!