Lots of lights

Who installed the new hybrid battery that you purchased? Does it have a warranty?

Based on everything that you wrote, it probably is a problem with the hybrid battery. You need to get the trouble codes read by a scan tool. Once you get the trouble codes, then you will know what the problem is.

 

Yes.. read the codes. Also typically the battery have at least one year warranty.

 

Having an oil change done in March is pretty much irrelevant at this point. Did you check the oil level when you received the car back?

That 'oil can' light (which I don't see in any of your photos) comes on when there is no oil pressure. No oil pressure means no oil. You need to stop running the engine immediately and do not run the engine or drive the car until you have checked the oil level on the dipstick. If there is no oil registering on the dipstick, add oil to the engine, initially 1 qt at a time, then check after adding each qt. Once you get oil registering on the dipstick, add ½ qt at a time, continue checking the level after adding each ½ qt. When the level is between ½ and ¾ the way up the dipstick, stop adding oil. Do not fill past the top F mark.

Usually, when that 'oil can' light comes on, damage has already happened in the engine.

 

That could be a pack problem, but as others have pointed out, you need to read the codes to be sure, and that must be done with an OBD2 dongle that can see all the ECUs.

New as in an OEM pack from Toyota, or as in a refurbished battery from "Joe's Bill'M and Leave Town Hybrid Batteries", or something in between, like GreenBean? Your options range from very good with the OEM pack to zilch for the fly by night pack rebuilder. Also some of the replacement packs use different chemistries or cell geometries. The proven gold standard for longevity are the Toyota prismatic modules.

 

^ This. As long as you have the oil pressure light appearing, or the red triangle flashing when turning corners, there is no other problem the car has that's important enough to spend time on. Deal with the oil problem, promptly, or no other problems will matter.

"No oil pressure means no oil" a lot of the time, but there can be other causes of no oil pressure. If the dipstick shows oil but the light still says no oil pressure, you still have an engine-destroying problem, that still needs to be found and fixed.

The only time the oil-pressure light does not mean an engine-destroying problem is if the light is coming on falsely because of an electrical fault in the oil-pressure warning circuit. That's like the coin-landed-on-edge scenario and it isn't hard to check for. Unless you check and find that, the oil pressure light is dead serious.

 

My bad, didn't read the entire first post to the point where the OP mentioned the oil warning light. The light wasn't in any of the pictures posted. That is probably a good thing (not being in any of the pictures), because if there was a hole in the pan, the oil filter fell off, or any other "lose all the oil once and for all" conditions that light should be lit all the time. Ticking is not a good sign though.

How common is an oil pump failure on this car? I don't recall ever reading about that happening in this car. It must be possible though, any pump can break.

Recent oil change was noted - maybe there is a chunk of plastic wrap in the oil filter, intermittently blocking the flow?

 

Checking the dipstick is always a good first idea, no matter how recently an oil change was done. What the dipstick shows might not be what you expect.

When the level gets low enough, the pump sucks air when you go around corners and the oil sloshes to the side of the pan, so you get flickers of warning at those times.

It's after you've checked the dipstick, and made sure it wasn't low, that you then start thinking about more complicated possible reasons for low oil pressure.