Hey RowbearYY,
It sounds like you're having an issue receiving Messages notifications on your iPhone. We can understand wanting to look into that further. We want to help.
You mentioned the issue only happens with BlueTooth enabled, if you have an Apple Watch, its possible the notifications are being sent to the Apple Watch instead of your iPhone. You can find more information on that here: Notifications on your Apple Watch - Apple Support
"Where notifications appear
Notifications appear on your Apple Watch or iPhone, but not both.
If your iPhone is unlocked, you get notifications on your iPhone instead of your Apple Watch.
If your iPhone is locked or asleep, you get notifications on your Apple Watch, unless your Apple Watch is locked."
If that's not applicable, we'd recommend checking to see if any Focus or Do Not Disturb settings are enabled that could be blocking notifications: Use Focus on your iPhone or iPad - Apple Support
Thanks!