Google Nest Thermostat tripping Double Pole 25A breaker
Based on your comment about the unit running fine after indoor temperature got closer to the setting. I would say that there is an issue with the auxiliary heat strips. They come on when the requested temperature you set is more than a couple degrees higher than the room temperature.
There is a high current draw to run these strips. They also come on when outdoor temperature is too low for heat pump to function properly.
Make sure the wiring feeding the heat strips is large enough to service the load they draw. Find a label that states the KW of the heat strips.  Then find what size breaker is needed to provide that.  It may be that the wire and breaker is undersized for the new heat strips. 10kw strips will often be fed from a 60 amp circuit.
Edit:  looking at your photo I see a double on the right bank labeled heat pump.  What does that feed? It looks like that is 30A for outdoor unit.
The 60a circuit should be powering the heat strips. It could be that your old thermostat was not wired to activate the strips. The nest is wired to turn them on but the 25 amp circuit is not able to handle heat strip load.  Some pictures of the air handler and how it is wired would help rule in or out this hypothesis.