Upgrade MacOs on older Macbook Pro

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

Monterey can run Safari 17.6 (released on July 29, 2024) – but not Safari 18.

Safari Release Notes | Apple Developer Documentation

That's probably not an issue, for now. If you do want, or need, browser updates, Monterey will probably be able to run the latest version of Firefox for a couple of years. (The current one runs on systems as old as Catalina.)

https://www.mozilla.org/en-US/firefox/new/

1. No.

2. For updates, generally not; it can still access many of Apple's online services.

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Do you have newer versions of macOS and/or iOS and have contact key verification turned on? that might explain your issue logging into Messages.