Just like all of you, I’ve been experiencing the same problems with an iPhone 7 (loaned to me by my daughter after a disaster I won't go in to, so that while we haven't been able to live in our house the last 5 or so months, I could call forward our home phone number to the iPhone) and with the automatic update 14.0.1 last Sunday, Oct. 4, 2020, which I finally had to use my MacBook Pro to finish the installation on Monday the 5th, the phone failed on Tuesday the 6th. The dreaded No Service alternating with Searching. I tried all the helpful hints, etc. I found online, all the suggestions, including taking it to my local Apple folks (an authorized Apple reseller, not a Genius Bar type), but balked at sending it in because my daughter said no, she hasn't had good response with being supplied refurbished crap (sorry, phones) that they send you in lieu of actually fixing yours. And it's an old phone with a tiny crack in the screen's corner which in no way affects the phone's usage.
ANYWAY, long story short (I know, too late!) My phone FIXED ITSELF! (Knock on wood) It's been having the quick battery drain so I had been plugging it in to keep it up, and last night I forgot, didn't plug it in, and it drained to 0% overnight. I plugged it in to the charger this morning, and at 3%, the phone started pinging (from messages and voicemails) popped back on showing my cell company's name In the corner, and working like it should.
So I'd like to add to the list of things to try - let your battery completely drain to 0%, then start recharging. Hope this helps.