I actually have a working'ish prototype of this project laying on my table right now.
It's a 120mm noctua fan being controlled by pwm i relation to the temperature. It also has an oled screen to show temp and fan speed. All controlled trough home assistant via esphome.
I say working'ish because the temp sensor i'm using (dht11) is unreliable and is messing up half the time, so i'm looking into buying a DS18B20 instead.
I'd be happy to share schematics and code if you'd like it.

If you want to do this as an ESP project anyway, you don't need the extra controller.

Fans take a simple PWM signal, which your ESP (or even one of the smallest Arduinos) can create easily.

I think pretty much any mosfet / h-bridge / motor control board with pwm should do.
If you have those 4-wire fans with a pwm input that accepts 3V3 logic, you might even be able to attach them directly to the ESP:

• https://github.com/KlausMu/esp32-fan-controller#wiring-diagram-for-fan-and-bme280

But that's not all fans, I had some mixed results with that.