I'm going bonkers trying to diagnose.
2002 4runner with almost 300K. I rarely drive it (I have a 5th gen I prefer to drive ;-) )
When I slowing back down the driveway, slight braking; I hear one single POP or clunk. Then, when driving forward, could be after several stop and goes...I hear the single POP or clunk when braking at a stop. This is always with the wheels straight... although, sometimes I can hear it when turning right. But basically, after the clunk in one direction of travel it seems to not do it again until I go the other direction.
Kinda like something shifted (which tells me a bushing or something suspension related). It is very difficult to test consistently.
I do not feel any vibrations in the steering wheel at any speed, always one single clunk (sometimes a small clunk quickly followed by a more dramatic clunk. but only once and a while)

More info and what I have done....
I have new tie rods and had an alignment. I have replaced the sway bar bushes but not the end links. The links 'seem' fine and tight. I replaced the disk brake pad hardware (pins and springs). This is not the pads hitting/moving. I know the driveshaft can exhibit signs of needing grease when coming to a stop, but this feels different. I greased the yokes/driveshafts anyway. My suspension bounces correctly when testing by pushing up and down on the bumper - it settles quickly and zero noises.

My only thoughts are: the CV axle may be in the early stages of wear. Or maybe the coil over 'strut/shocks' are in early decline. But I don't want to through money at parts that aren't actually bad. I may need to take to a shop to see if they can find the issue, but hoping to figure out without paying someone to pin point the issue.
Any thoughts? Anyone have the exact symptom?

Can you confirm which end/side the sound is originating from?
May be worth checking your rear control arm bushings?
100% certain your spare is cranked up tight?
Munched body mount bushing(s)?
Hitch bumping the bumper?

Oh yes, sorry. It is most certainly in the Front of the vehicle. (hence all the focus on items in the front that I am checking). It does not seem to be one side or the other. Too difficult to tell where. Tell me more about "munched body mount bushings". I checked several, but not sure where they all are located or how to tell if they are 'munched'. I looked for dry rot, used a pry bar on so many bushing areas. Can't seem to locate an issue though.

Have you tested your drive shaft U-joints.
Simple test procedures are on line?
Are you in 2WD or 4WD when clunk?

I have a failed body bushing/bolt at my feet that gives some feedback when I
goose the throttle sometimes. I suspect the chassis flexes a bit on the frame
and allows a momentary gap to come back down onto.

Other front items to consider are any/all the A arm bushings.
at 300K they are almost guaranteed to be fried in some capacity.
Did you also replace the swaybar frame bushings? They could be
allowing the bar to squirm around?

Always in 2WD.
When rolling back down the driveway, I have even tried it in neutral - same clunk as i gently apply the brake. I guess the driveshaft still turns in neutral though. I have grabbed the driveshaft to check for any play. nothing moves. So I suspect the u-joints are good. And the noise is JUST once. never constant.

Yes, those are the bushings I was referring to. But I have not replaced the sway bar END links. But I've pried and grabbed them - there is zero play/movement.

I used a pry bar on the A arm bushings too. no give. The sound/feeling is almost as if something is shifting a little bit. So that has me also thinking some bushing, somewhere. I checked all the bolts too. but maybe there is one I am forgetting to check.

Let us know what you find. I have the same clunk. Low speed, backing up or forward and going up drive way and rear articulates. Mine sounds like the right rear. It’s like something is shifting into/out of its spot.

All bushings look good. Been chasing it for about 6 months. I just turn up the volume of the radio but would be nice to know what the deal is.

Possibly U joint, also another thing to consider is the slip joint on the rear driveshaft. The splines could have wear. If the rear suspension bushings are original this is another possibility.