n8n is the practical replacement: a visual workflow builder with a large connector library that you can run yourself. Huginn is the older, more programmable option for people who would rather describe agents than draw a flow.
What you are replacing
Zapier's advantage is the connector catalogue and the fact that a non engineer can build something that works before lunch. Self hosting swaps a subscription for a service you now operate, so the saving is real only if the automations matter enough to maintain.
It models automation as agents that watch, transform and emit events, which suits monitoring and scraping jobs better than a linear flow does. For people comfortable in code it is more expressive than a canvas.
What it does not replace
The project is older and the interface shows it, and the connector library is nothing like Zapier's. This is the option for someone who wants to build the integration, not pick it from a list.
Stay on Zapier when the automations are few, the data in them is not sensitive, and nobody wants to be paged because a workflow runner ran out of disk.