It's not *precisely* made to replace Trello, but Obsidian has a great Kanban plugin that behaves very similarly to trello. I combine it with the Tasks plugin to give each card/task more functionality. The Tasks plugin has a querying syntax which you could theoretically pipe into other API/scripting plugins. I can't say for certain "Adding this tag to a Kanban card can produce an API call" but I wouldn't be surprised if it's possible. I haven't looked that hard.

If you aren't aware of Obsidian, it's a plaintext/markdown-based notetaking app at its core, but with an extremely deep set of community plugins. The notes/boards can be synced via any local/remote cloud, or with their paid service.