2019 Toyota RAV4 - Loud transmission

transmission .loud lack of insulation under hood .radio acts up

Did you notice the transmission noise when you test drove it or is this a new problem? If you bought it new it should still be under the bumper-to-bumper warranty. In any case a Toyota dealer is your best bet.

New car with a warranty. See your dealer.

Additionally, how has the OP determined that the transmission is the source of the noise, rather than the engine? Or, is the problem simply the result of a lack of insulation under the hood?

This–as well as any engine or transmission problem–will be covered under the terms of the manufacturer’s warranties.

The 2019 gets the new 8 speed transmission and it has not been the best. Quite a few have complained of its shifting. I had a rental and if this was my car, I would have driven right back to the dealership. Even my kids in the back seat complained of the jerkiness and they are used to being in my stick shift car.
If you look on the RAV4 forums, people have found ways to add under the hood insulation. This helps with the engine noise, but not the transmission shifting. You can ask the dealer for the transmission as I think there is a TSB to reprogram the transmission.