Therefore, if I understand correctly, the player already has the best volume normalizer, so all I need to do is tag all my audio files with it?
Yep.
And since you are not a bot: welcome to the forum Neovolter
Also,
this forum search method may come in handy to learn more about MusicBee, loudness normalisation, EBU R128 and whatnot.
(it exclusively searches the MusicBee forum)
edit
Don't blame yourself, this is confusing stuff for sure.
The rsgain tool you found indeed mentions ReplayGain 2.0. But it uses EBU R128 as the core algorithm.
So both MusicBee and rsgain are using the same industry standard to get results.