Kagi chrome extension doesn't set Kagi as one of the available search engines on Android

Steps to reproduce:

Install Kagi chrome extension on an Android 12 phone on either Chrome or Samsung Internet browser
Go to search setting in the browser and look at the available search engines
Notice Kagi is not there

Expected behavior:
Kagi should be in the list of available search engines

Debug info:
Tested on Android 12 on a Samsung Fold 3 5g on both Samsung Internet and Chrome.

@pixel Could you verify if this is supported by these browsers?