I think a product search would be a nice feature. It certainly is possible. I’ve had a little go making a basic one myself (more proof of concept at this stage but it works).
It’s pretty basic but it pulls the list of articles for my shop as an XML document using the speadshirt API and then extracts all the product names along with their price and product ID and then creates a list which you can search from. Using the product ID’s it composes a link to the product page on the site.
I am using this plugin for my store at https://www.littlegreendude.com/shop and my initial concept search for it is at https://charliecallow.co.uk/lgdstore-search/
