I encountered an issue where a Shopify store had set in-store pickup as an option for various locations, but but was no longer visible at checkout as option (it had been working previously).
So they were expecting to see a Shopify checkout like this:

But instead, they were only seeing the “Ship” option, like this:

The issue where the local pickup in-store option is not appearing at checkout may occur due to a deactivation of a pickup location and the subsequent transfer of inventory. To troubleshoot this, follow these steps:
Navigate to Shipping and delivery in the admin panel. Scroll to pickup in- store and click on the location. Turn off in-store pickup. Save. Turn in-store pickup back on. Save. Now do a test transaction with a product available at that location and when you get to the checkout, you should should see the pickup option for that location. Repeat for the other locations as appropriate.
Yes. It’s the old “Turn it off and on again” advice. You’re welcome! 😀