Heater only puts out heat when car is accelerating

More then likely you have a restriction in the heater core or are low on coolant. When you accelerate you are pushing more coolant through the system.

If it were me, I would pressure test the cooling system after you make sure it is full. Make sure there are not leaks and then I would replace the heater core.

https://www.2carpros.com/articles/radiator-pressure-test

https://www.2carpros.com/articles/car-heater-not-working

Normally we would need to do a little more testing before we do this just to confirm it because it is a pretty large job. However, it is pretty clear that would be the issue and on your vehicle it is not difficult. I attached the procedure.

If you would like to confirm it, use a laser temp gauge on the heater hoses going into the heater core. Clearly they should be about the same. If not then you have a restriction in the heater core.