There are some powerful Shopify apps that can help you improve the product findabitlity. These plugins allow search by product tags, types, options, metafields and show the matching variant image with search terms
You can try Dynamic Search Placeholder. It is released by the Craftshift team, is an important tool for all Shopify e-commerce administrators to offer dynamic search ideas to the customers. With Dynamic Search Placeholder, you are enabled to fetch entirely all titles and tags of products in an automatic way. Furthermore, you can employ those keywords to switch your static placeholder to various dynamic search suggestions. Then, as a result, this extension will totally make changes to your search box placeholder within a few seconds. Additionally, as an administrator, you can simply and quickly change the keywords in the app page. There is a fact that people tend to feel so confused that they do not have any idea of what to search on your store. Do not worry, this extension will definitely inspire them by offering various dynamic search ideas. No more hesitating, let Dynamic Search Placeholder be your productive, unique tool now with just 1 click only!
You can get the app here.
There's a great search app called Smart Search by Searchandise that I think will suit your needs. The app features instant suggestions, autocorrection, synonyms, redirects and stopwords along with. a comprehensive filtering option on the collection pages of your store as well.
For example: price, availability, vendor, product type, tags and reviews, collections, etc.
If there is anything else I can help you with, please let me know.