Yes, it should be available soon on the Play Store :)

Additional suggestions, you can also search using npub (nostr public key). Usually it will be faster to search using npub compared to username.

This is what Vitor said at least v0.23 has already implemented better search function. You better try to update the latest version. Let's see if you still have problems. I can find you by username search.

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What is the version of your Amethyst? Currently v0.24 , the latest version has improved the search functions

It is probably because of their clients. What is their nostr client?