Not technologically, not neatly, but true DIY :)

As a rule, a mechanical timer equipped with a power regulator has 4 wires. 2 of them are responsible for turning on the turntable, lamp and magnetron (for a common disconnector), 2 more are used to control only the magnetron.

The power adjustment on the mechanical timer is carried out by controlling the operating time of the magnetron.

(https://flamingo-nn.ucoz.com/load/mikrovolnovye_pechi/ustrojstvo/ustrojstvo_mekhanicheskogo_tajmera_svch_pechi/60-1-0-620)

Therefore, if you want to control the power of the microwave, you need to install 2 relays. One will be responsible for the general activation, the second will be responsible for controlling the magnetron.

I didn't need power control, so I closed the magnetron control contacts between each other and set the relay to short the wires of the general power supply.

I soldered the encoder to the breadboard and made holes in it that match the regular holes in the housing of the microwave oven. Using brass spacers, I set the optimal height so that the handle does not stick out of the case.

If you want the timer to stop when you open the microwave door, either add a separate endstop and connect it to the arduino, or use an optocoupler to connect one of the endstops that are already in the microwave.