Display gallery dynamically by category

Challenge: I would like to create galleries dynamically based on the tag or category assigned to images.

This issue comes with two problems.

Problem #1 is the media library in WP does not allow for categorization of images nor does it allow for tags. I would like to be able to assign multiple categories or multiple tags to images.

Problem #2 Example of challenge. I am working on a website for a customer that has a sign business.
Coroplast (corrugated plastic) sign can be used in multiple locations (possible categories) such as indoors, outdoors, standup, dye cut. It is temporary signage.
Aluminum signs can also be used in multiple locations such as indoors, outdoors, or wet areas. Permanent signage.
MDO primarily outdoors made from heavy duty laminated plywood. Permanent signage.

I would like to be able to assign multiple categories or tags to each image and then allow the user to click on the category thumbnail and display different signage that applies.

Example they click on “outdoors” they would get aluminum images, coroplast images, and MDO images. If they click on “permanent” they get a gallery with aluminum images and MDO images.

I’m on a tight budget this is a startup business. Free would be optional or a one time payment plugin.