Profiling with F3+L outputs many errors to log

When you start profiling with F3+L, the game output shows this error many times:

Tried to pop one too many times! Mismatched push() and pop()?

It ends with it saying the profiling results could not be saved.

This is very similar to this other report MC-267308 that seemingly got fixed in 24w33a, where the game had to be frozen. The same behavior is happening here, but the game doesn't need to be frozen.