The only minor hiccup I have had is that at some point the devices decide that enough time has passed that there must be a software update available ... and I ignore the prompts to do so ... which is fine ...
... but then there was a power outage and when they powered back on they were in some update status where they weren't online until I clicked something ? I forget ... might have been an updated google legal agreement with the update ?
They are google pixel devices with stock OS load and no apps added (other than that SMSForwarder) but even still, had some logic for software update that produced a minor annoyance.
Working well, albeit the Google login tends to give more problems than it should, in smaller and independent apps like these.
But I definitely observed that the one time that I left the phone plugged in for the most part of 3 months, the battery never was the same. It lost like a third of its capacity.
No battery swelling?
I copied the idea and did the same, it's essentially free of cost to do so where I live, thanks to having operators that offer a pay-what-you-use tier with no fixed monthly cost. The line is just to act as a 2FA mule, so it means it costs nothing (save causing any kind of expense once every 6 months, but sending a single SMS does it, so I guess it actually costs something like 20cts per year)
Apart from the SMS Forwarder app [2] you suggested, an HN commenter [3] provided links to some FOSS alternatives which I didn't get to try but they should work fine and are ad-free.
[1]: https://news.ycombinator.com/item?id=28251107
[2]: https://play.google.com/store/apps/details?id=com.frzinapps....
[3]: https://news.ycombinator.com/item?id=29711030