Thank you for the proper details, it helps me a lot to understand the problem.
I believe there is actually a solution for this. It may not be perfect, but I think it should be better for your expectations. So, what you need, is basically search the product categories related to each product – so the 'paint' products within the 'paint' category will show up. And also, these should be ordered by these categories by relevance. This is all possible, and I already made the following changes on your back-end:
1. I have configured and enabled the Index table engine – this is very important, as it makes the search much faster, and more precise, and allows better searching for taxonomy terms (product categories).
I will rahter not go into details on how I did it, if you are interested, then you can read more about the index table engine in these documentation chapters: Index table engine documentation & chapters
2. I have increased the 'terms relevance' so that if the phrase matches a product category, related to the product, it is moved to a higher position in the results list: https://i.imgur.com/hqwCSqV.png
This means, that the plugin will now prefer results based on the product category names, and will more likely place them at the top positions, if the search phrase matches them. This might not be perfect in every case, but it should do the trick.
If you try 'paint' or 'acoustic flooring' there is a very high chance that the plugin will return more accurate results.Best,
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