Need router with SIM

I think I’ve asked this before, but I can’t find the answer, sorry.

I’m looking for a router to use instead of an ADSL one. The usage is sporadic, and the monthly cost of ADSL is unreasonable in this case. My thought is to go for mobile data instead, using a pay-as-you-go SIM.

The main use of this is in a building that is used intermittently, but then quite heavily (online games or movies for example) and where the mains power is turned off when it’s not being used.

Many of the options are battery powered, and my previous experience of these is that if the power is turned off long enough for the battery to go flat, they will not start up immediately when the power is restored, sometimes needing manual intervention. I need this to be seamless, so either no battery option (just like an ADSL router) or software that works immediately.

An ADSL router with SIM backup would be OK provided it will work with nothing plugged into the ADSL port. I’m intending to cancel the phone line once this is in place.

Can anyone suggest something that they have experience of, that will work here?

They aren’t cheap, but have a look at the 4G routers by Teltonika.
I’ve used them for various setups across the UK.

They are rock solid, robust and will connect automatically as soon as power is connected. (They don’t have a battery)
You can attach an external aerial if needed, they have wifi built in, as well as several wired sockets.

https://amzn.eu/d/aM5n3Dx

I’ve not tried configuring one using a RISC OS browser though.
(Not sure if that is a requirement?)