...is that better to plug the charger and stay in this situation(so it wont use battery)?
That is not guaranteed. Under extreme high-demand conditions—like gaming or using FCP—that tax both the CPU and GPU—the computer may need extra power and will draw it from the battery to augment wall power.
That was detailed in a very good Apple tech article that we lost during the "simplification" of such material at the Altar of Minimalist Design some years back. I have no reason to think that useful adaptation has been deleted from newer models.
Many 13-inch Macbook Pros have but one cooing fan. All notebook computers lack the big fans and open airways of a proper gaming computer. I lost my first Macbook Pro to overheating of the GPU during gaming.
Performance: the heat management system in your computer uses sensors to monitor the temperature of internal parts. If those start to heat up, the system signals the fans to increase speed to a level needed to maintain safe temps.
If that fails to reduce temps, then the processor may clock back to reduce heat production. In a worst-case scenario, the computer may shut down to save its brain. Constant exposure to high heat can reduce the service life of most components.
Like Servant of Cats. I and not sure of the current upper critical internal temp for Apple notebooks are. For years it was around 100°C/ 212°F.
Chill pads do not work well on Macbook Pros made since about 2009 (the "Unibody" form factor). Prior to Unibody models, the processor heat sink contacted the case bottom making the bottom of the case part of the heat dissipation system. Chill pads made a big difference.
However, on UniBody Macbook Pros, the logic board hangs from the upper deck and cooling the case bottom is far less effect.
Have you read this Apple article on Apple notebook computers and temperatures?:
Keep your Mac laptop within acceptable operating temperatures - Apple Support
Ambient room temps specs for operating the device are here:
MacBook Air (13-inch, M3, 2024) - Technical Specifications - Apple Support
We don't know your Macbook Pro model but I believe all share that Operating Conditions spec.