If you want to integrate the results into Discourse’s search itself, I think you can still use algolia, but that solution requires a lot of effort(e.g. how does one prioritise which results from which sites are shown, and is the right metadata easily available and always up to date?) and is an additional cost(algolia licensing).
A free, low maintenance and effort option, which directs users to external content is the Advanced search bar extension which we commissioned Discourse to extend a few years ago. Basically if the external site is using standard url queries for their search, it is compatible with this option.
By this i mean, do their search urls look like this?
