02 RAV4 starts normally but makes loud whirring sound for a couple seconds after engine fires, as if whirling starter motor just disengages loudly for some reason. At least that’s my only thought. Have heard of this before in RAVs of this vintage. Gonna need a new starter soon? Or worse?
On my daughters 2004 Rav4 the return spring on the ignition switch got weak and caused the switch to not return to the run position after starting. Could also be a weak spring in the starter. Next time it happens try quickly turning the key left and see if that works. If it doesn’t it is probably the starter.
It does sound like the starter motor isn’t disengaging and turning off like it should when the key is returned to “on” from “start”. Could be an electrical system problem like the key switch as noted above. But it could also be the starter solenoid contacts are sticking closed. This can be a very bad thing as if the contacts stick in the crank position for a long time it could start a fire in the engine compartment. So whatever’s the reason, it needs to be looked at by a shop straight away. Suggest to not park this vehicle inside or near buildings until you know what’s causing it. Note that what you are hearing may not even be the starter motor. A good shop should be able to listen to the sound and tell you if its an emergency situation or not.
I am going to guess this is a semi stuck VVTI valve, a well known Toyota issue. Google and watch the youtube videos and see if it is the same noise.