I'll admit that I don't fully understand how manifold pressure and RPM can be used to find engine power output
That's because it can't
That sort of statement, stated in isolation, is simply wrong. Engine power output comes from the chemical energy in the fuel. Not from the air!
The first step is to establish what the fuel flow is. If you run rich of peak then not all the fuel is getting burnt, so that makes it harder.
If you run at peak EGT or lean of peak then all of it is getting burnt, and the engine power will be proportional to the fuel flow.
(The fuel flow v. power output line won't pass through zero,zero on the graph because the engine needs a certain amount of power to suck the air in, and to overcome friction, etc. Have a look at some engine performance graphs from e.g. Lycoming)
An engine running as above, at a given fuel flow rate, will develop much the same power at any reasonable RPM; all that happens is that at a higher RPM the torque will be lower (because HP = revs * torque) and at a higher RPM it will try to suck in more air (because the whole bit of the engine before the inlet valves is just a fancy air pump; the more you rev it the harder it will suck) so the throttle needs to be closed more in order to get back to the desired power output.
MP is a crude indicator of torque and this is why it is relevant to engine
management but it is nothing to do with determining what the power output is.
There are tables showing that a particular engine, at a given altitude, with a given MP and at a given RPM, will develop X HP. That is probably what is confusing you. These tables "work" because that particular engine model will have a particular carb or a fuel injection unit bolted onto it, and these accessories will be set up at the factory to deliver a certain fuel flow rate at a given airflow, and the airflow obviously depends on the altitude, the temperature, the engine suction (RPM) and how much that suction is constricted by the throttle valve.
Also the vast majority of light planes don't have a fuel flow rate indicator, which is probably why we have these tables.
If you have a plane with a decent fuel flowmeter then (when in cruise) you just set the engine up at an RPM which gives a nice engine life, say 2300, set the MP for a value which is within limits for that RPM (because MP is a crude indicator of torque i.e. crankshaft stress, there is often a limit on the MP at a given RPM), say 23", and then lean the engine so the fuel flow gives you the desired power setting.