Search via dynamic tag cloud. How?

In short: I’m looking for a plugin that provides search via a dynamic(!) category/taxonomy/tag cloud.

Details: I’m working on a site which holds a very large number of posts of a custom post type with quite a number of taxonomies attached. I want to allow the user to easily drill down into this content by providing a filter form, containing all tags of all taxonomies as toggleable buttons, displayed in a tag cloud of sorts, also showing the use count for every tag within the current search result set. Clicking a tag adds it to the filter and the search result display should update, now showing only post matching all current filter tags. That’s as far a I got.

The difficult part: The filter section should update as well and, in addition to all active filter tags, only show tags that when added to the filter would result in a non-empty search result. In other words, tags, who’s use count within the current search result set is zero, should not be shown.

Clicking an already active tag again, should remove it from the filter and everything should update accordingly.

Here’s a website using such a filter: https://www.arroway-textures.ch/textures

Such a dynamic tag cloud filter basically is the only way I can think of to provide the full set of tags to the user without search fields or list boxes, which are very inefficient in cases with several taxonomies and hundreds of available tags.

Unfortunately, I wasn’t able to find such a plugin. Some seemed to come close, but none provided the dynamic tag display. If anyone could point me to such a plugin or knows of a different approach to get the same kind of efficiency, I would greatly appreciate it!