This issue started earlier this winter. When I start the car up, if I press the brake pedal with a medium/firm foot, the engine rpms will fall and jump. If I take my foot off the brake pedal or just barely touch the brake pedal, the idle smooths out. After the car fully warms up this becomes less of an issue.

I do hear a rattling/patter/putting sound from under the dash when the car is cold. It goes away or fluctuates when I apply the brakes.

When I step on the brake pedal with firmness, I hear a whooping (air escaping) sound from under the dash.

The brakes perform very well. I don't feel any loss of braking power.

After the engine is off and the car sits for a few hours, the pedal is very firm until I turn the engine back on.

I've replaced the vacuum valve on the front of the brake booster.
I've replaced the vacuum line on the front of the brake booster going to the intake manifold.
I don't have any other leaks.
I've checked/swapped both my ICV and AMM.

Do I have a faulty brake booster?

Thanks,

Mike