Apache mod_auth_form sends POST to intercepted reverse-proxied request

From the documentation:

When the end user has filled in their login details, the form will make an HTTP POST request to the original password protected URL. mod_auth_form will intercept this POST request, and if HTML fields are found present for the username and password, the user will be logged in, and the original password protected URL will be returned to the user as a GET request.

I have an running at port 45001 and apache reverse-proxying to it. I use form authentication and ErrorDocument to enforce login. This is my config:

<VirtualHost myip:44302>
    ServerName myserver.com

    # Pass auth info
    RequestHeader set X-Remote-User %{REMOTE_USER}s

    # Login page is directly on the server - don't use reverse proxy
    ProxyPass /login/ !

    # Proxy all requests to the app running in a docker container
    ProxyPreserveHost On
    ProxyPass / http://localhost:45001/
    ProxyPassReverse / http://localhost:45001/

    # Require auth for all requests except the login page
    <LocationMatch ^/(?!login).*$>
        AuthType form
        AuthName "login"

        AuthFormProvider ldap
        AuthLDAPURL <url>
        AuthLDAPBindAuthoritative off

        # Redirecting to login page if auth is needed
        ErrorDocument 401 /login/index.html

        # If authorization fails, return 403 insead of 401
        AuthzSendForbiddenOnFailure On

        # Use session cookie
        Session On
        SessionCookieName session path=/;httponly;
        SessionCryptoPassphrase <passphrase>

        Require valid-user
    </LocationMatch>
</VirtualHost>

Form (simplified of classes and div wrappers):

<form action="" method="POST">
    <input name="httpd_username" type="text">

    <input name="httpd_password" type="password">

    <button type="submit">
        Login
    </button>
</form>

For other scenarios, where I don't use the reverse proxy, the workflow is correct:

1. access URL
2. check for the session cookie
   1. request login if needed
   2. send HTTP GET request to the original intercepted URL

But when I use the reverse-proxy, instead of sending HTTP GET to the intercepted request, apache sends HTTP POST. The app behind the proxy doesn't work with POST and prints an error.

If the user refreshes the page, it all works correctly because the session cookie is already set.

What's causing this misbehavior and/or how do I properly configure this authentication to work?