I have the exact same problem after updating to ios 14.1 and 14.2. Also tried all the different ways to fix the problem without any result. I'm using a iphone 7 and the temporary fixes usually last for a day or so.

For the people who want to have a fix. I disabled 'VoLTE' as described by other users inside this forum and i have not had the problem since. You can disable the setting inside settings>Mobile Data>Mobile Data Options>Voice & Data . This can only be done when 4G is selected. I'm using a iphone 7 and im still on ios 14.2. I hope this will help some people.

@rwillett Have you tried a hard reboot? by holding down the lock button and the volume down button. Your phone might connect again and you will be able to change the setting I had the same problem with the error in my mobile data menu saying i needed to update my software or my carrier data. The problem usually went away for a while after hard rebooting. Eventually i used DFU mode to reinstall ios 14.2 which still didnt work, but after disabling 'VoLTE' the problem just dissapeared.