I want to make it so any time someone clicks any of the "Push settings" buttons for any of the indexes, the settings are merged and pushed instead of outright overriding everything.

I am not convinced that it is known that the buttons override values manually set via the Algolia Dashboard with whatever defaults are set via the plugin. I am also certain that there are potential cases of teams mixing the two together, and that's a recipe for disaster.

So if at all possible we should fetch a given index's settings and do the necessary logic to determine which setting fields are not the default values within a fresh index, and merge those in to the local, to-be-pushed, settings values that are default.

Questions needing answered before we can start anything here, is how to handle situations where both remote AND local settings are not defaults, which value "wins" ? Perhaps retain current situation and let the local version override? Log the situation and inform the site owner? Prevent the submission of the settings push until they have made a decision and removed the conflict?