Speedometer stopped working mid-drive then after stopping at stop light car would not shift out of first gear

We were driving like normal, had it in cruise control, when suddenly the speedometer went down. It fluttered back on and off a few times, but eventually shut off completely. Actual driving wasn’t hindered while this was happening. When we were forced to stop at a stoplight it didn’t come back on and we were stuck in 1st gear for the rest of the drive. Tachometer still works, gas gauge still works, but the indicator for what gear it was in wouldn’t light up either.

Check engine light only came on for a minute or so at the end of the drive (probably because the engine was starting to heat up due to not being able to shift up gears) and turned off after letting the car rest for a while before checking it out.

Checked transmission fluid, looks good.

Looking up stuff online and calling a mechanic seems like it’s a speed sensor (output speed sensor specifically). Does that sound correct? How would someone go about pinpointing and diagnosing it?

And how easily is it fixed? Could any auto repeat mechanic do the job justice?