In previous versions, while recording was in progress, I could select a portion of the audio being recorded and save that selection as a separate file, while the original recording continued.
In this way, I could work with that section of audio, on another PC, without stopping the recording (long recording sessions).
In Audition 2022, the "Save Selection" option is greyed out. It is only available when I stop recording.
Is there anything I can do to enable that tool?
I'm afraid that option hasn't been available for a while. I may be mistaken, but I think that the last version you might be able to do this with is Audition 3. The entire engine's been rebuilt since then (more than once) and I think that it's a consequence of that.
Steve_G is correct and the reason is to ensure that all resources are dedicated to recording and nothing else interferes with that