That looks really pretty to be honest, I really like it. There is a sort-of similar example with ajax search pro here: https://ajaxsearchpro.com/staff-search-filter/
However there is an issue yet to be resolved, that currently it is only possible to have 1 filter box per taxonomy. In your case that means, that all categories would be under 1 drop-down. This would be only possible with either custom fields, or if the terms were separated into more taxonomies.
I am definitely adding some sort of feature in a future release to allow creating more filter boxes per taxonomy. It has been requested many times by now, but I could not work out a proper solution that is compatible with previous releases as well.Best,
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