I hope this helps some people. Pay attention: I've been using MacOS since 1994, and iOS since 2009.
THIS CAN'T BE FIXED. For most people, this can't be fixed by turning off Bluetooth, or toggling the 'hide alerts' switch, or anything else.
Please don't waste hours of your life trying to fix this, I've done that for several years so I can report back and tell everyone else not to.
There isn't a solution here in 85 pages of comments, stop reading and go play outside.
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Background info:
Since I've had my iPhone 8, I've been unable to leave Bluetooth on and also get iMessage notifications.
Since iOS 14, I never know if I'm going to get them.
I know what I'm saying - I work with iOS, Android, Ubuntu touch, macOS, Linux, and Windows. I've built several computers, modified GPUs, put custom firmware on routers, cameras, and God knows what else. I can fix a lot of things, but not this.
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Fun tip: I've found that when you've just met someone, it's really easy to get them to believe you didn't get their messages because "Bluetooth was on" or "I don't know what happened." And people you're dating think it's hilarious!