Transmission worries

I do not think that you caused any harm to the transmission. @ChapmanF will be able to answer.

 

Can't drive and Park maybein zB mode . You've hurt nothing. It's all pretty stout in there.

 

Can you give details of what made you think it was in Park?

The car evidently didn't think it was in Park, because if it had, it wouldn't have gone anywhere.

So, something else is what was happening. But I can't really speculate on whether the something else did or didn't do any damage, without a better idea what the something else was.

 

I press the Park button to convince the transmission system to go into N when I'm bored of using R to do so at speed.

Unless you heard sounds: your transmission was not in Park. The pawl is engaged by a BLDC motor atop the transmission; there would be lots of warning lights if it had unintentionally done the park routine described here: The Toyota Park-By-Wire System Explained: A Walk Through the Park - Automotive Tech Info

 

If the vehicle senses it is moving through the wheel speed sensors, the Park pawl will not engage .... if it did, the sudden stop when the park pawl engage would probably snap a driveshaft or CV joint .... I've exploded one of those on the Taxi Prius trying to get out of way of oncoming traffic, it hit the bitumen and bang clunk clunk clunk as the balls fell out, and no drive anywhere Flat tow to the workshop so I could replace the driveshaft

T1 Terry

 

Surely you just use the joystick to select either D or N (has to be held at N for some 2-3 seconds) in such circumstances. It wouldn't be good practice to hit the P button while going at any speed, regardless of the in-built protections of doing so, which might allow it.