That’s a very good idea. For the engine to idle & run smoothly all the spark plugs, injectors, and pistons have to be working equally. If one injector isn’t spraying as much as the other, that could cause a symptom like this. So an injector cleaner treatment is a good idea. If it seems to help, but not enough, try it again.
There’s a fuel system test OP could have done too, called in injector balance test. Howw it works in principle, imagine you had 2 small leaks in one of those metal tanks used to hold compressed air. You wanted to know which was the bigger leak. So you’d block both up with your fingers, then pump the tank to 100 psi, then remove the block of leak 1 and time how long it took for the tank to go from 100 to 90 psi. Then you’d pump the tank back to 100 and do the same thing for leak 2. If it took 1 minute for leak 1, and 2 minutes for leak 2, you’d know leak 1 was twice as much as leak 2. Same thing can be done to test the injectors by pressurizing the fuel rail and using an injector pulsing gadget.
Checking the compression for the proper amount, and balance cylinder to cylinder is a good idea along these lines too.