Electrical – Ground wires: Do I have this right

I have 200A load center with a solid bare #6 ground wire tied to a ground rod. Ground/Neutral are bonded in the box.

Then run stranded #6 (does it have to bare?) to the 100A auto transfer switch. Ground/neutral are seperated. Ground bonded to box and neutral isolated. Do I also need a solid bare to ground rod? It’s right next to the 200A load center.

Next run stranded #6 (does it have to be bare?) to the 100A sub-panel down line from the transfer switch. Ground/neutral seperated. Ground bonded to box and neutral isolated. I do have a solid bare to ground rod here.

Can I use stranded between boxes?
Does it have to be bare?
Does each box have to tied to ground rod?
Am I missing anything?

Thanks for your help guys.

The meter box is connected to the 1st ground rod with #4 uninterrupted solid. The subpanel is connected to the meter box with #4 solid. They are back-to-back (the subpanel used to be the main panel). I have since isolated the neutral in the subpanel.

The NEW main panel is connected to its own ground rod with #4 solid. The neutral is bonded to ground.

1. Do I need to run ground between the NEW main panel and the subpanel? (Subpanel is currently grounded to the meter box)
2. Do I need to run ground from the NEW main panel and the transfer switch/ transfer switch to subpanel?
3. Do I need to run the transfer switch ground to the ground rod? (Neutral is isolated)