How do I make both channels same volume?

Audacity doesn’t do anything in real time—during the recording.

I can think of a couple of ways of automating the balance. Install Chris’s Compressor…

…and run it on each side after you split them. If you change the first value, Compress Ratio from 0.5 to 0.77, Chris will simulate broadcast compression including auto volume.

It’s a little more work, but you can apply the AudioBook Mastering tools to each side. Their job is to force whatever you have into the restricted AudioBook Format including loudness.

It’s only three tools, but one of them is custom.