Erlang and Elixir do not include a trust store. The Hex client does, as explained in the README file, and there is a package on Hex called certifi that is used by the Hackney and HTTPoison HTTP clients.
BTW, I haven’t looked closely at the Java code, but I believe it does more than just verify the certificate chain: it also checks for a certain hostname in the peer certificate SAN extension (in Erlang 19.3 you can use :public_key.pkix_verify_hostname(cert, dns_id: 'example.net') for that), and uses the certificate’s public key to verify the request signature (use :public_key.verify/4, avoid using :crypto directly)
