Perhaps part of the issue is how power meters measure power?
To my knowledge, they basically use average torque multiplied by average angular velocity (RPMs) measured several times per revolution but typically recorded at intervals of once per second.
Given the way that suspensions work, I wonder if it doesn’t take higher peak torques (more effort) to achieve the same average torque and therefore the same measured power.
We know that times are basically identically with identical measured power, so measured power more or less equals output at the wheels, but we also know that energy IS being lost to heat, because physics.
We just don’t know how much, or whether it it’s significant. It certainly feels significant, especially when riding hard while standing up, which makes the suspension stroke the most.
(Sidenote: This discussion ignores the fact that pedals aren’t the only way in which effort can be (usefully or not) input into a bike suspension… but you shouldn’t really be riding with so much weight on the handlebars or saddle anyway.)