How do you power a rocket engine?

Wouldn't the pressurant/backfill gas dilute the propellant as it was added?

Only if the pressurant gas dissolves into the liquid propellant. Even then, it doesn't even dilute it per se, it just makes something akin to rocket-fuel-soda which causes all sorts of flow problems in your feed lines. Naturally, if your propellant is stored as a gas, adding more gas to pressurize will of course dilute it as you say, but I've never heard of something like this.

So the short answer here is: no, it won't.

A rocket engine is more properly referred to as a chemical rocket engine.

One thing I always wanted to see was a close expander cycle areospike. The reason is that expander cycles are heat limited. Areospikes biggest negative is that they require more cooling but if you are heat limited that is an advantage.

You could make the highest possible thrust expander cycle and it would be high efficiency upper stage for early staging as you don't lose efficiency by staging early.

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Another thing that jumps out at me is that its really sad development on the F-1 and J-2 stopped. The mentioned J-2S never flew. The US had this amazing technology stack, F-1 + variants, J-2 + variants and Apollo stack.

Instead of keeping around a Saturn 1B type vehicle with the Apollo on top they threw literally all of that stuff in the trash and started new with Shuttle.

But non of that new Shuttle stuff is better when thinking about it end to end. Because of Shuttle SkyLab could not be saved and because of Shuttle SkyLab 2 wasn't launched.

The US with the Apollo stack and incremental updates could have dominated in space.

A complete and utter mismanagement of the investment that was made during Appollo.

Perhaps, being pragmatic, tweaking existing designs was not going to put more money into the R&D of Yoyodyne [1].

[1] https://en.wikipedia.org/wiki/Yoyodyne