I had a very similar washer I think, from the 90s, and it eventually started exhibiting the exact same symptom (sometime in 2020 during the COVID crisis). I followed the same process and the blog author, but when I opened the transmission, the problem was immediately apparent: the large "spin gear" was plastic and was completely worn down, the teeth did not engage at all anymore with its driving gear.

Unfortunately, I found Maytag did not sell any separate parts for the transmission, only the whole transmission, for somewhere around 300$, which was more than the 25-ish years old washer was worth to me. People frequently bash manufacturers for using plastic parts like, as a mechanical engineer, I think there may be valid reasons for the design choice, but knowing the part is subject to wear, it should absolutely be made available as a spare.

I ended buying a new washer, from a very limited selection of models that were available in the summer of 2020 shortage of just about everything. I gave away the old one for free, the guy who picked it up needed the motor to repair another machine, I hope he was able to use the parts to keep it running for a long time.