The last 1.x version specifically doesn't seem to do this on Google searches. In addition, the old version did not require you to change your default search engine to one you don't use. This is because they changed their framework:
> We've updated the Kagi Search for Safari extension to be cross-platform, using Safari Web Extensions instead of Safari App Extension framework. This will require you to grant access to the Extension on the search engine during your first run. See the instructions in the app for details
> - [Fixed] Redirects should not experience intermittent failures
> - [Changed] You can override which search engine redirects to Kagi manually. The first time you install/ upgrade to this version, the extension will attempt to detect your current Safari search engine
> - [Changed] You only need to provide extension access to urls on the search engine you are overriding.
The last 1.x version specifically doesn't seem to do this on Google searches. In addition, the old version did not require you to change your default search engine to one you don't use. This is because they changed their framework:
> We've updated the Kagi Search for Safari extension to be cross-platform, using Safari Web Extensions instead of Safari App Extension framework. This will require you to grant access to the Extension on the search engine during your first run. See the instructions in the app for details
> - [Fixed] Redirects should not experience intermittent failures
> - [Changed] You can override which search engine redirects to Kagi manually. The first time you install/ upgrade to this version, the extension will attempt to detect your current Safari search engine
> - [Changed] You only need to provide extension access to urls on the search engine you are overriding.