Those endpoints are only available through the HTTPS due to two reasons: 1. it involves sending a string of password, which wouldn't be encrypted* over Gemini and 2. it involves two fields of text, and Gemini can't do forms (and by extension, multi-field input) as HTML does. Searching/Composing works in Geminispace because it's a queryString being sent with the request, but a complete form (such as that from a login page) would need multiple queryStrings.
One possible solution (and an idea/suggestion for Midnight Pub's bartender/developer) would be an authentication flow through Gemini client certificate tied to/interchangeable with the HTTPS passwordful login. Currently, Midnight Pub only allows for passwordful authentication, which limits the authentication flow to the HTTPS protocol only.
Client certificates for Gemini is something I only got to discover yesterday by using a fediverse platform here in Geminispace, it's very interesting to use. Gemini browsers (such as Lagrange) allow the user to quickly create a certificate ("identity") with commonName and additional, optional fields (such as emailAddress, userID, organization, etc), which can be tied to an authentication flow within a Gemini capsule.
Every certificate is a pair of a public and a private key: the user signs a request with their private key and the remote peer is able to check the signature against the public key, thus proving the identity. Every Gemini communication happens through SSL/TLS tunnel, so nothing is needed to be activated except for a manually-built client certificate for a domain, which is simple as e.g. "Identity" menu -> "New Identity for Domain..." menu item in Lagrange.
As for the availability of Midnight Pub's source, I don't know.
Editing to add observation regarding the excerpt "involves sending a string of password, which wouldn't be encrypted over Gemini": while the Gemini client-server comms are encrypted (tunneled with SSL/TLS), the string would be part of the URL instead of something like a "POST body". That's why I stated that "password wouldn't be encrypted over Gemini".