The Toyota dealer put 5w-20 oil in my 4runner which calls for 5w-30 (listed on the cap too). They didn't even put full synthetic like we talked about. I wouldn't have even known if I hadn't looked at the receipt and asked the tech directly about it. They claim they don't carry 5w-30 anymore and told me its all the same, no issues. Is this bad for my engine?
Oil
Double check your manual and/or updated guidance from Toyota.
Toyota retroactively made some oils compatible with their engines.
For example, my 2004 Prius which requires 5W-30, was retroactively made compatible with 0w-20, years later. Both oils are fine for my Prius, and I’ve switched back and forth between them. And my Prius now has 299K+ miles with the engine running great!
Not sure if this is the case for your vehicle, but more likely than not, it should be okay. Of course, research your specific year and model.
Use whatever your owner's manual recommends and nothing else, to be safe. I accidentally used 5W-20 once in a 5W-30 engine, when I realized my mistake, I immediately checked my technical service bulletin, it was backward compatible with 5W-20, but my engine used slightly more oil than normal. It's a '99 Ranger with 292k miles on the clock. I switched back early and it's been fine ever since. Just use whatever you find in your service manual.
Probably it would not hurt your engine if you use it for one cycle only. Since it is still bit cool outside, 0w-20 should be fine for a while. But if you car requires 5w-30 you better switch back to it again on your next engine oil change.
20 and 30 are indicating upper temperature limit your oil can operate. Usually it is good to use what is required and by time upper limit can be increased (by time means in 5-10 years from car manufacture date). Decreasing the upper temperature limit is not recommended.
Oil viscosity when it's cold means it's a 0W or whatever. At operating temperature the weight equivalent is XW-30, meaning there's 30-weight oil inside the engine. It's not based on operating temperature. The operating temperature is constant, no matter the temperature outside. It takes longer when it's cold, a 0W may work. It's supposed to be -30 when it's at operating temperature and nothing else. There is almost no need to put different viscosities in a modern engine. All it will do is wear it out faster.