My advise is stick with what you have as far as the modem/router is concerned.
Most TV's only have 100Mb ports. They don't need to do anything higher than that.
Just bought a 55" LG CX OLED (2020) and it has a 100Mb Ethernet port.
I expect the 2021 model to have the same.
Curious what high bitrate 4k that the LG supports that you can't play with 100Mb/s?
politely, I'm afraid your partially incorrect - having had this TV 2 years I can tell you a few won't play - forget compressed streams, I'm on about remuxed rips direct from the original 4K disc - especially if they used a 100GB disc and not a 50GB disc (fit more detail/info with higher bitrates on 100GB discs)
to note: a REMUX is when you rip your original 4K disc BUT only pull the 'untouched movie from it' (not further compressed in any way so it's exactly like having the movie there), leaving all the rest of the crap behind, allowing you to store it on a NAS drive or PC HDD and stream across the LAN so you can watch without swapping discs AND they stay nice n new (unscratched) on the shelf...
E.G. would be the new remaster of LAWRENCE OF ARABIA in 70mm (remuxed only) or a REMUX of something in
Dolby Vision that was put on a 100GB disc (less compression from the raw footage in the "cutting room"), try streaming a remuxed rip of those from LAN PC to LAN LG and you will see it buffer and freeze - this is because action sequences or lots of screen movement can take the bitrate much higher than 100Mbps...some can even go into 200Mbps for a quick second or so - see AVforums for more info on this...
as for the FRITZ router,,, there are reports of people getting higher syncs than that of the one I have.. comes with tons of software too..i know it doesn't mean I will - but worth a blast if u can get em cheap enough, and if crap just re-sell it