It sounds like that Arkenfox-like setup is clobbering Split Browser on the disposable side:
That shouldn’t be necessary. The configuration values in the higher-numbered 22-firefox.bash will essentially override those in the lower-numbered 21-tor-browser.bash in the same directory.
Is there really no firefox-bin executable inside the Firefox directory? What Firefox build is this?
If the persistent side is based on debian-11-minimal, install the libnotify-bin package to get notify-send. (Although given how many dependencies that package pulls in, maybe just switch the persistent side to a non-minimal template instead.)
No, by default it would be the PID of the split-browser process. But it’s a moot point: After amending that Arkenfox-like setup you won’t have to invoke split-browser-bookmark manually at all, nor mess around with environment variables.