I thought this was already the case, but apparently not. I could not find another post requesting this, so I suggest:
If I start watching a live TV show and while viewing I decide to record it, I wish the recording would include the portion I was watching before selecting to record.
Looking at the Activity Icon, I can see the “Recording: Live TV - Session”, so possibly rename that portion of the recording to the actual program name and continue recording the remaining portion of the program?