Categories and tags on portfolio subpages (or other)

First thing I can suggest is that for complex filters this is a great option (it is an affiliate link):
https://www.squarewebsites.org/squarespace-plugins/universal-filter?peachs_apc=zygmunt-spray

As for how to set it up, this plugin may help with the lightbox element, but it may become difficult to manage.
https://www.sqspthemes.com/plugins/ultimate-squarespace-lightbox-plugin

The "auto-layout" list sections might be a reasonable way to layout the content, but they're not (as far as I'm aware) compatible with the universal filter plugin from SquareWebsites. So you may want to consider the portfolio page instead of the blog as both of those are filterable, but that has limitations in terms of number of pages and content on the landing page, no excerpts etc. Despite the blog item pages not being as flexible to set up, they are likely to be your best option.

This is an interesting problem to solve, lots of options, none perfect, different limitations etc.