The meaning of thermal throttle counters and package power limit notifications in Linux

When the core is throttled it means it is slowed down (voltage lowered, frequency lowered) to cut the heat being generated (the heat comes from the power and the power is proportional to the square of the frequency). I am guessing the package throttling means that the piece of silicon the core has been placed on is overheating (rather than the core itself) and so once again voltage has been lowered.

This certainly has a negative impact on performance.

Ways to avoid are (a) don't run such compute heavy applications (at least not all at once), (b) check your cooling mechanisms (fans etc) are working and (c) operate your machine in a cooler environment. It's possible that none of these are doable/fixable/broken in your case.