Vent Hood and Inline Fan Control - Intercepting PWM - I think

I’ve recently made some updates to my home and have a puzzle to solve.

I have 2 bathrooms and a kitchen that share a vent stack. There is an inline fan located below the roof
and each branch has a damper. The inline fan is an Infinity AC fan controlled by ESPhome. The fan works well and the bathrooms have been easy to both automate and create manual controls.

For the bathrooms I have low voltage switches connected to an ESP32 that when toggled opens a particular damper. The opened damper triggers another automation that powers up the inline fan to about 40%. This has been working great, but now I need to add some control to the kitchen vent hood.

What I’d like to do is use the touch screen of the vent hood to send signals to my inline fan and dampers, bypassing the hood’s builtin fan. I’m hoping there is a way to intercept the pwm single from the hood and use it to send commands to the inline fan. There are 6 speeds on the touch screen.

Does anyone have an idea on where to begin with the project? I was thinking of first trying to figure out what PWM signals are being sent by the controller, but I have pretty limited tools. I don’t have an oscilloscope. Only a basic DMM. Most of my searching leads to creating a PWM from ESPhome, but not intercepting/interpreting one. To get the Infinity running I needed to create a pwm, but now I can just control it from HA. I’m hoping there is a way to read that the hood wants level 1-6 and I can automate accordingly.

Thanks in advance.

Edit: i realize that the controller might not be using PWM. I’m not sure. Attaching the wiring diagram.

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Not sure if you’ve seen this but it may give you some ideas/leads.

This cheap logic analyser was recommended to me a while back and it’s worked well so far. I haven’t used it for PWM though. It can be used with Sigrok.

AU $7.78 14%OFF | USB Logic Analyzer 24MHz 8 Channel 24M/seconds Logic Analyzer Debugger For ARM FPGA Logic Analyzer Logic 24M 8CH
https://a.aliexpress.com/_mOuGQtq

Thank you for the links! I’ll have a look at that project now.