What seems to be a real difference from the OP's description was that for me the PCB of the left button/scroll wheel was not glued to the housing. I only had to remove the 3 screws from the PCB and it came off. Then it was possible to solder all 5 switches on this PCB (left button, forward and back buttons and the two buttons of the scroll wheel). Here are two pictures, showing the PCB in the original and the removed position.
I can't seem to see it in your photo, does the weel use a standard encoder? you know, this(
https://www.amazon.it/BIlinli-Encoder-Decoder-Altamente-Logitech/dp/B08FTD65KG ). I am looking to buy one but I don't know if I can get over a mushy scrolling wheel