Ho to assign items to specific offline stores and show product availability on product pages?
Product Conditions
The Store Pickup with Locator extension allows assigning locations to particular products if they are available only in specific offline stores. This can be done with the help of product attribute conditions in Content → Locations → choose the location → Product Conditions.
This way, the customer will be offered to pick one of the stores, where the product is available during checkout.
Keep in mind, that to make product conditions work, you need to enable the Check Product Availability in Stores on Checkout and Cart option in Amasty → Store Pickup with Locator → Configuration → General.

MSI Source
The Store Pickup with Locator extension also provides the functionality to display the Product Availability block on product pages. This block provides the information regarding the offline stores where the product is presently in stock.
The locations list works in conjunction with Magento MSI functionality and will appear for products, assigned Stocks of which are associated with any available Location's Source:
Only locations where Product is In Stock would appear by default.
To implement this block, make sure to assign the needed sources to locations and enable the Show Relevant Locations List for Products with Assigned MSI Stock setting in Stores → Configuration → Amasty Extensions → Store Pickup with Locator → General.
In order for the MSI feature of our extension to function correctly, it is crucial to create a new Stock (apart from the Default one) in Stores → Inventory → Stocks and assign sources to it.

Once this is done, run a full reindex and flush the Magento cache.