Intermittent Misfiring with no Overheating

IMHO; you need to test for head gasket failure; BEFORE throwing parts and extra work at this problem.
How many miles and how long have you had this car?
Do you check the fluid levels at every fill-up and has the coolant level been going down?
Could someone have put stop-leak in the coolant to cover-up this problem and now that 'patch' had fallen off?
Your dealer doesn't know what they're doing - don't waste your time & money there anymore.
These cars usually seep coolant into the combustion chamber when engine is cold, which causes a misfire during start-up. When the engine warms-up, the aluminum expands and seals the coolant seepage. That's why your problem is intermittent and only during start-up. The dealership has a TSB on that and should know better!! Did they sell you the car and don't want to repair it under warranty???? Find a Prius specialty shop for proper diagnostics and documentation.

Pull the spark plugs, check the tips and borrow a borescope to check the pistons for steam cleaning.
You need to do a compression and leak-down test, WHILE the engine is cold. The 'car care nut' YouTube channel has the procedure.
The different coils is an indication that someone has already tried fixing this problem without proper testing and diagnostics. In other words throwing parts at the problem, hoping to fix it that way. TESTING is the only way to nail-down a problem, rather than blindly throwing parts at it. Those aftermarket coils tells you that someone has already done that and that the problem is persistent..

Good Luck....

 

What’s the miles and how long have you had it?

head gasket failure is VERY common 3rd gen and Prius v problem.

 

You have a head gasket leak, I would say with 99% certainty.

It sounds like your "dealer" is not a Toyota dealer or the mechanics are young and inexperienced.

White smoke and overheating are typical for most cars with a blown head gasket but not a gen3 Prius.

The fact yours is rattling everytime the engine engages means it is likely to strand you soon because the hg leak is advanced.

A high quality borescope inspection is a definitive test but throwing more parts at it is foolish. Before long the parts would cost as much as a head gasket and sometimes a replacement engine.

My guess is they want you to trade it in on a new car and give you a token $1500 for the v.

Find a hybrid shop. You don't want to pay a dealer for a hg or engine replacement. Or trade it.

Car Care Nut HG Borescope at 660s

South Main Auto
Excellent Borescope Footage at 6:50
Honda Misfires on Coldstart Only

 

All gasoline has additives to clean fuel injectors, often called "detergents". As a result fuel injectors rarely get clogged no matter which gas is used.

Some brands are known to have better cleaning additives with Chevron's often testing best. Most brand names justify higher prices by using more additives than necessary and call their gas "top tier" because of the increased additives.

However engines which build up excessive carbon, primarily due to oil burning, can not clean their excessive carbon buildup with additives of any strength. Additives will keep the back of the valves acceptable if the engine is port injected (which sprays fuel of the back of those valves) and is not an oil burner.

For an oil burning gen3 with low tension rings it takes a teardown or careful walnut blasting to clean the valves.

In more recent engines with exclusively Direct Injectors pumping gas straight into the cylinder, no additive can do anything to the back of the valve. As a result Toyota now uses dual injection in the latest gen5 Prius and the last two Rav4 generations to name two.



Bottom line

All gasoline has additives to clean fuel injectors and it works as designed. In a good engine with port injection, it will keep the back of valves acceptably clean.

If you want a cleaner gen3 engine, mechanically repair oil burning when present and then change oil every 5k.

or better yet

Buy a Toyota with a dual injection engine.

 

Ask the mechanic that's working on the car; Does it look like "Stop-Leak" was added to the cooling system? If that was done; you may experience additional issues, down the road - like overheating issues. You haven't ran that car in the hot summer months, so you don't know. The temperature lamp in your dash lights up around 248+F, when the engine should be running around 185F-205F. You could be operating that car at 245F, all day long, without knowing it. That's hot enough to start breaking things, like head gaskets. You've got a large car driven by a small 1.8L engine. That electronic engine coolant pump is a silent killer of these cars. That should also be checked out and possibly changed while it's out of commission.
Most people will install a P10 HUD to monitor engine coolant temperature, so they don't break anything. Think of it as an early warning system.

Good Luck...