Are you sure the original fob battery is the slim CR2016, as there are 2 other slightly thicker ones, CR 2025 and 2032.
Just a thought regarding internal contacts...
Oh, you bought one, but happy you will install better quality tyre than when it was new.
Look for the encircled "E" on the sidewall, it means it is approved for European use.....????
Could be, kids of today have their heads stuck in smartphones, they spend hours tweaking their gray cells learning how to use the things, plus the games they play must also stimulate that gray matter....????