It began as an occasional creak, groan or rattle when I pressed down on the fender behind the headlight. Occasional.

Now, I hear it most times when the car comes to a stop and the inertia forces a slight dip.

Or I just tap, tap, tap the brakes and you hear a groan, creak or rattle. But not always.

No sound when the wheels are turning. None of the classic wheel bearing noise at medium to high speed.

Some part of the suspension system?

Shocks would be my first guess....front suspension from there.

Probably the upper shock mount. You should plan to replace both of them if one is bad. DO NOT overtighten the shock nut when you reinstall, if this ends up being your problem.

I'm impressed with the lifespan of some of the multitude of bushes on these cars. There's a few to check, if you can get it on a ramp or stands can help see if there's play.
A long pry bar to lever against suspension components can speed things up.
Front AR bushes that hold it to the subframe can and do start to make noises, if you have some spray grease, try in on those 2 first. Access by removing the undertray.
Shock mount upper, lower shock bush, check the condition and for play.
Subframe bushes, inspect each side inboard and out of the rear donut that bolts to the lower part of the chassis behind the front axle. Top bolts tight inside the engine bay?
Check the front disc shields have nothing trapped. Wheels road balanced, maybe an alignment check.
Top and bottom wishbone bushes, the pry helps eyeball any movement.
They shouldn't groan, just waft.