I've sent numerous feedbacks to Apple. Many others have contacted support and gone through the usual troubleshooting. There's no real solution. This thread has pages and pages of users and their interactions with Apple tech support. Apple is aware of the issue and the 14.3 release notes had it listed as being addressed but it hasn't been completely fixed.
I will say that it doesn't happen as often but it does still occur. Also, I'm only speaking to sms/imessages. This is not about any other apps that have issues. My guess is that developers of other apps that are affected by this bug are waiting on Apple to correct their IOS software first.
Lastly, it's been mostly confirmed that Apple engineers do NOT read these forums. These forums are for us as users in the Apple community. Sending feedback or contacting Apple support is a sure way for Apple to know about issues such as this one.
I'll list it again, the only work-around I've used that is dependable is to either back out of the individual text window and stopping at the main chat window OR completely killing the chat window (swipe it away). Both of these options need to be performed after every single text (sent or received) but only if you're not going to stay in the chat window watching it and be actively engaging in texting that same person. If you're in an active text conversation with the same person and you get a text from a different person, it's possible that you won't know about the other text that you just received. Yes, it's very annoying and extremely inconvenient for relationships and businesses.
Hope this helps.
IPHONE-12 Pro Max running 14.3 but I first encountered the issue on my IPhone-X when I installed IOS 14.