I am guessing here because so much information is lacking…

I assume this car has loads of miles… 150K plus… Right?

I will guess it uses a quart of oil every 2000 miles, or maybe 1500 miles, or even 1000 miles. Which is it?

If the engine is burning oil, that can foul the spark plugs and cause a misfire that can be cured with new plugs… The car uses more oil, fouling occurs, new plugs. If the same cylinder misfires every time, that one cylinder’s rings may be worn out so oil consumption won’t be super high.

If an injector is getting stuck and dumping extra fuel into one cylinder, that cylinder can misfire when the plug fouls from excess fuel. A check engine code for “rich mixture” should be set as well as the misfire code.

Have a compression test (wet and dry) on the engine. If that shows OK, you might assume it is the injector or injectors.

A good mechanic would have already done these tests (but not for free…) or at least suggested them. If yours did not, find a better mechanic!

Unlikely the valves dropped far enough to bend anything. Broken valve springs will make the engine misfire at higher rpms. A boroscope in the offending cylinder would show contact with the pistons and a compression test would confirm or deny bent valves. Even so, removing the head for a complete service would fix it. Cheaper than an engine.

Stop using the dealer for repairs for a 7 year old car.

If you can find a YouTube video that shows step by step how to change the lock actuator, go ahead and give it a try. The tricky part of this type repair is to remove the door panel without breaking something. There is nearly always a “secret” screw hidden in a non-obvious spot that can cause you to break something.