I'm Miles from the Social Care team at Shopify. Thanks for reaching out. I'd be happy to look into why your collections and products aren't showing as expected. When a collection isn't appearing in the search, it may mean you've added an automated collection. Creating an automated collection involves setting up conditions to match the products that you want in the collection. For a collection to appear in the search option, it would need to be a manual collection.
To find out the type of collection you've created, head over to your Shopify Admin and click Products > Collections. Click on the collection and scroll down. If you see a section called "Conditions", the collection is automated. If conditions don't exist, then you're dealing with a manual collection.
From your post it sounds like you have set up automated collections, so you will need to set up conditions so your products can be added into each collection. To learn about setting up conditions, I recommend checking out this guide. It will walk you through how to use conditions in your collections.
If you're unsure how to move forward from here, please let me know.