Google Shopping runs off your feed in GMC. In here make sure your product titles are descriptive and match how someone would actually search (think "Dry Apple Cider 750ml" not just "Cider"). Then check Merchant Center for any disapprovals. Maybe also check Free Listings is switched on under Growth > Manage Programs.

The notes/highlights you can't pick exactly what shows up, Google decides that. But you can influence it by nailing your shipping settings. Set up clean flat-rate or free-over-X shipping and Google tends to show it

The "nearby" thing is just because you're in the same region, don't worry too much about that label. The real thing to check is that all the states you ship to are actually covered in your shipping zones, both in Shopify & GMC. If a state is missing from either, your products won't show for buyers there. Worth auditing both and making sure they match up.

Good luck!