Problem with wrong Mobile Data settings, already by default

Since I upgraded to an iPhone 13 Pro, 5G service is often unavailable and just Edge is working. Now, the issue is still present and got even worse on my 15 Pro by occurring daily. 

I found out that the reason must be based on incorrect settings of APN etc. in the mobile data network. 

During a trip in Japan I used an OCN data SIM, the corresponding APN settings were installed via a config profile. My mobile network settings in iOS are always incorrect since then, so I have to change them manually. 

I deleted the OCN profile already years ago, but when I tap on "Reset Settings" in the mobile data section, the wrong settings immediately show up again. Also "Reset Network Settings" or backing up in iCloud and restore doesn't fix the problem.

I found one thread here where somebody had the same issue, and it was suggested to build a custom config profile with the correct APN settings. I did so, but cannot install it, the phone says there is already a profile installed. But no one is listed. So it maybe wasn't uninstalled completely - is there any way to reset or overwrite the "default" settings, or any other ideas which could help not ending up in giving up my 16 years old backup? 

I tried everything stated in the article provided by Apple. 

As it says "To revert to your carrier's default APN information, go to Settings > Cellular > Cellular Data Network > Reset Settings. If you installed a configuration profile, the profile's default information will be used instead." and that is the case, old settings from the former SIM are used, which were installed via profile. The problem is just that now no profile is installed.

My current carrier doesn't provide any profile, the correct settings are to be set automatically. The hotline suggests to ask Apple for support, they think it must be an iOS bug.

What I tried in addition was to uninstall the eSIM profile, and redownload it. Also, I put in a different physical SIM card. But in both cases, the settings were still the "wrong" default ones...

It’s now getting really annoying, the only workaround to force the iPhone to get 5G instead of Edge, is to turn off the eSIM and then back on again. Sometimes more than once a day…

Is there any option to fix, eg override, the default settings back to “normal”?