can the ground for the driver be shared with the ground of the AC circuit?

No need to. That way the there is complete isolation between the AC and DC circuits.

 

Although this switch will be replaced by an SSR, I’ve considered this issue: can the ground for the driver be shared with the ground of the AC circuit?

If you use a SSR there is isolation, no problem. Probably 2000 to 4000V of isolation.
I don't know what power you have in your country. The "cold" side of the power line is not really at ground. It could have some voltage on a good day. It is too common for Line and Neutral to get wired backwards. You should consider either wire of the power line might be at 120 or 220.

I placed this snubber because

Snubber on DC often have a diode. Snubber on AC do not.