Turntable channel imbalance

Your turntable is very old and basic. You only live once. Get a Pioneer PLX500 for $370 or a PLX1000 for $700 and enjoy life. Add an Audio Technica AT95E or VM540ML or Nagaoka MP110.

I do use an AT SS445E/U high-end NOS cart with original Nude 0.3mil elliptical stylus. I feel like I’d have to spend a bit to get better performance, no?

https://www.vinylengine.com/ve_downloads/index.php?audio_technica/audio_technica_ss315e_335e_445e_en.pdf

You say it's only present on some LPs.  This suggests it is either in the recording of those LPs or is an artifact of your own experience of listening to them.

But it's simple to check your system piece by piece by channel switching and substitution.

First, are you getting differing volumes on sources other than the record player?  If not then that exonerates everything beyond the phono amp.

So, starting with the cartridge, choose the LP that displays the imbalance characteristic the worst and plug the R phono output into the L phono amp input and vice-versa.  Is the quiet channel now the other one?  Then change the whole phono leads R to L and vice-versa.  If the quiet channel remains the same then this exonerates the cartridge and the phono leads from cartridge to phono amp.  If the quiet channel changes on the first test, then you need to check the cartridge.  If it changes on the second you have a problem with the quiet channel phono lead or its connectors at each end or those sockets.

Then check the phono amp and its leads to the pre-amp in the same way.  If the quiet channel changes then the issue is in the phono amp or its lead or connection out.