Do you also have an Apple Watch? Check out - Official Apple Support Article HT204791 (for example: support[dot]apple[dot]com/en-us/HT204791).
That Official Apple article clearly states, "Notifications go to either your Apple Watch or iPhone, but not both." and that, "If your iPhone is unlocked, you'll get notifications on your iPhone instead of your Apple Watch." - and furthermore, "If your iPhone is locked or asleep, you'll get notifications on your Apple Watch, unless your Apple Watch is locked with your passcode."
I have reproduced this behavior with iPhone 12 Pro running iOS 14.6 and Apple Watch 6 running watchOS 7.5..
I will take a wild guess that your iPhone is trying to send the iMessages and/or other Notification to your paired Apple Watch, but eventually gives up (times out) and finally gives you the Notification on your iPhone.
I urge you to file a complaint or at least submit feedback with Apple to allow DUAL-NOTIFICATIONS on both the Watch AND the iPhone for iMessages simultaneously, and hopefully with enough complaints they will add this obviously highly desired behavior of NO DELAYS if the WATCH it out of range or otherwise just to make sure you get the text message.