Using RMS normalize with normalize tracks independently selected is quicker (no splitting) & more accurate.
The height of the peaks (“peak amplitude”) is not a very good measure of loudness. It’s quite possible for a stereo track to have higher peaks in one channel than the other and both channels sound the same loudness. If it sounds balanced, then I wouldn’t worry about whether one channel looks higher than the other, after all, it’s what it sounds like that matters.
Most recordings are balanced by ear so there will be variations from record-to-record but the variations will be random so if all of your records are higher in the left or right channel there’s probably an imbalance in the playback system.
Most modern recordings are probably digitally limited so you’d have matched peaks on the digital version but the record cutting & playback process can change the “waves” so the peaks on the record may be altered. Of course, if all of your records are higher in the left or right channel there’s probably an imbalance in the playback system.
After RMS Normalize run Amplify or regular peak Normalize (both channels together) to make sure you’re not clipping.
I think most phono cartridge specs allow about 1dB of channel imbalance (if they give you a spec at all). The left & right preamp channels won’t match exactly, the ADC probably has some channel variation, and the anti-skating adjustment on the turntable may have some effect. Welcome to analog!