...but OTOH I doubt this test can help to fix the problem. The said SIM card is the only one that has also a data plan booked by me (the other one is just voice and SMS only), so I suspect that as soon as this card gets activated in the phone, it tries to connect to servers in the Internet, but since there is another setting in Android to enable/disable data services (and since it gets enabled by me only on demand), then its connection attempts of course fail, but that dumb program seems to try it endlessly. This is just my attempt to explain it, I'm not sure b/c it all happens under the surface, ie. in the background, there is no indication in the GUI nor in the log(s) [also maybe due to the fact that it fails and it only logs successes, if any...].
There is a setting called "Data usage" under Settings. There the two SIMs appear, and under them is then a setting named "Cellular data" for enabling/disabling. Ie. only after manually activating here does data connection to Internet work. In my case this is disabled by default and gets activated by me manually only on demand. Other than that I'm not aware of any other setting that says "always on". And: I also have not installed any other program beyond the built-in standard defaults on this phone.
The setting I mention is burried in the settings menu. It isnt about data transfer it is about keeping the data connection open even when no data is being transferred. However its no use to you. I found it and it is a device level setting, not sim. Another possibility is one sim is set to not use roaming, and is trying to work off a tower further away.
Found a suspicious setting: Settings / Security / Apps with usage access / Google Play Store was enabled all the time (ie. "On")! Now I disabled it and testing... After 1h: LOOKS GOOD SO FAR!...
I've Data roaming disabled as it brings the warning "Attention! You may incur significant charges" when activating it. Btw, this error happens at home...