Sticky, shiny, oily dashboard

I've had 9? Gen 2s. None have ever experienced what you describe. Are you sure you don't have a heater core leak that's getting antifreeze vapor on the dash?

Anyway, these dashboards are a dime a dozen at salvage yards and can be replaced in less than an hour. If you're not a DIY guy, there's probably a hybrid shop in your area that would be familiar with it.

If you get a dash from a salvage yard, cars with the JBL stereo system have a speaker in the dash mounted above the center display. Non-JBL cars do not have this speaker.

Hmmm, after re-reading the post, are you talking about the upper glove box door?

 

Yeah those are the '06 up panels I like the painted panels better I put those in some of my '07s and '08s and that burgundy color looks like aluminum paint or something. But I see a lot of these cracks around the power button and on the other side lower glove box door in general in the southeast because of the heat and I imagine where you are in Texas this must be really bad I generally don't park my cars in the sun just to avoid stuff like this I mean I seek out the shade when I go to the store there's still some left and some parts in North Carolina shade that is. But you can get all of those panels from junkyard cars but I guess in your area some of them may look like this if they sit outside in the sun.

 

I don't know here in North Carolina which gets quite hot and dry the good portion of the summer hours have done amazingly well on the dash pads the tops even the upper and lower glove box and usually the panel that has the start button We generally try to park in the shade when we go out and when the car is on property it's predominantly in the shade would it lot in that. So other than some fading on the outside being it's out in the UV and ozone constantly reasonably acceptable but the insides even the leather perforated seats have held up amazingly well I've seen other units similar to mine and they're almost trashed and I'm buying our cars from towing lots and stuff like that.

 

Toyota & Lexus Melting Sticky Dashboard Lawsuit
Toyota and Lexus Melting Dashboard Lawsuit Filed, Again | CarComplaints.com

Neither mention the Prius though. I wonder if these surfaces on the OP's car were ever treated with something like Armor All and that is migrating out of the treated plastic in the heat.

Come to think of it, when we bought our 2017 used from a Toyota dealer they had treated the dash and some other interior plastic parts in some wayto make them slightly shiny and oily. If I had to guess, it was some type of silicone oil. Whatever it was it eventually evaporated (probably to concentrate in our livers...) over the next year, and now the dash and other parts have the usual sort of not oily plastic surface.

 

If it has been sitting a long time shake it vigorously then open it and make sure it hasn't precipitated inside. It might be necessary to poke around in it with a stick if it isn't clear.

Why? I had a bottle of PlastX in the garage which almost completely separated into solvent and insoluble gunk. It felt normal (but pretty empty) when it was shaken, and the stuff which came out was still the right color, but it was almost all solvent, and it ate the clear coat on the headlight to which it was applied.