P0A80 code + engine misfires?

Most likely separate issues.

 

It's possible that your 12vd battery is bad instead of the larger traction battery- but yep.......if your traction battery is original then it could be the "Replace Battery" code.


I'm a little more concerned with the misfires and rattling under the hood.
I'm not aware that a knackered traction battery will cause those symptoms.

Google: "Prius Death Rattle" and check your coolant level soon....like when you read this.
If at all possible, stop driving the car immediately.
Coolant loss can cause an over-temp issue which can damage your engine in seconds.

200,000 miles is a good run.
Usually the head gasket fails before then.....

 

On initial startup an early head gasket leak can cause a lot of misfires with resulting severe rattles and not set a code.

The logic at startup requires several misfires in the first 1000 revolutions to set a non-illuminating pending code (1st trip).

A second sequence of 1000 revolutions with misfires has to occur again (second trip) to set a current misfire code.

The coolant needed to cause a cylinder misfire can be counted in drops and often stops misfiring in a few seconds. At first the misfire rattles are occasional and do not occur on every startup.

Normally an early head gasket leak has burnt off the coolant before the second trip and the engine runs smooth with no misfire code.

A coil, plug or injector as the root cause of a misfire continues and easily codes.

As a hg leak becomes more advanced the misfires might last long enough to code and eventually the engine will show coolant loss.

An articulating borescope is an effective hg diagnosis. Compression, leakdown, combustion gasses in the coolant and coolant in the oil testing usually are not good enough on these engines.


Borescope tests should be run on a cold engine with the coolant system manually pressurized.

Car Care Nut HG Borescope at 660s

South Main Auto
Excellent Borescope Footage at 6:50

Articulating Borescope on Amazon