Updated December 4th, 2021
An alternative to Shopify pickup & delivery is to create a custom shipping rate for pickup. Compared to the Shopify pickup option this can be simpler as it doesn't require the customer to re-select a pickup location and it can work with custom locations as well.
Navigate to the Shipping and delivery settings to create a new profile.
Add the products you want to be available for pickup, create a shipping zone, and then add a rate. When adding the rate the name you give it will be the name that shows in checkout.
View your changes in the Shipping portion of checkout.
https://community.shopify.com/c/shopify-discussions/local-pickup-not-working/td-p/808991