Is managing recovery/fatigue just by TSS accurate enough?

Your Garmin probably just saw that you did more work than usual, and wants to bring it back down.

With recovery, I still believe we ourselves know better than any metrics. Do you feel tired? Is your motivation low, or are your legs heavy? Signs you need rest. The difficult bit is that pushing through a bit of fatigue is actually an important part of training, but pushing through too much is not helpful or even damaging.

That said, and in response to the title - for me, Trainingpeaks (TSS-based metrics) usually gets it right: if it says I need extra rest, I usually feel tired too. Any rides then just turn into a slog.