Kagi will not search via the Return key on i(Pad)OS if Settings > General > Search Suggestions is enabled. It just does nothing, unless I select one the suggestions.
I am also seeing the same thing as shurik: touching the magnifying glass searches using the search box input, as expected. This is a change from the previous behavior, where Return would always initiate a search.
I've tested this on several iPhones and iPads, with the same results. Solution appears to be either to disable Search Suggestions, or to use the magnifying glass instead the Return key. Very inconvenient, either way. Looks like a bug, either in Kagi or 26.4.1.