My question is, is there anyway on the router to see the speed increase without doing a physical speed test?
The router doesn't know or care as the only limiting factor on FTTP is the profile the ISP set.Technically, everyone on FTTP gets 2.4Gbit down 1.2Gbit up at the ONT, its the profile that restricts your time share of that to what you paid for.
Depends on the technology and ONT they are using mind you - some are XGS-PON, but the principle is indeed the same. It's just a speed profile set on the OLT and there will be no way for a CPE to know how to interrogate this.
Not on BT though.