how a signal for which calculate RMS can be filtered and have a fast settling time?
I believe you are running into stability issues in an output power control loop design.
See below a diagram of similar power control loops that I have implemented, where for stability reasons any filtering in the loop is minimized and only done with the loop filter itself which is designed for stability. The noise you are trying to filter gets filtered by the loop bandwidth itself.
The diagram below is very simple to implement (first order type 1 loop), where the accumulation of the derived error sets the loop bandwidth by adjusting K.  Make K very small for a long averaging time and better filtering but slower response.

Ultimately if the trade of filtering versus response time with a simple implementation like shown above is insufficient, you can change the loop filter to be a PID loop. This would more complicated and require more understanding of control loop design and a more detailed loop model but give you better performance in noise filtering versus response time. Essentially the accumulator (I) shown above would also be summed with a proportional path (P) and a derivative path (D) all with different gain weights and followed by a second accumulator for a second order type 2 PID loop.
Once a loop model is created, the modeling of the response time and effective filtering is very straightforward with tools such as Matlab, Octave or Python. As an example of the design process, below shows the loop model for the Power Control Loop given by the block diagram above along with the modeled response times versus K:


The above case results in an open loop gain given by:
$$G_{OL}(z) = \frac{0.83155K}{z(z-1)}$$
Below demonstrates given the Matlab and Octave code snippets how simple it is once the model is established to create the step response for the loop. Note the overshoot indicative of a higher order loop- this is due to the parasitic $z^{-1}$ in the digital loop implementation, and with a high enough K the loop will be unstable (unlike a true first order type 1 loop). Similarly the noise bandwidth, etc is easily established and optimized.