In the interest of not using anything that is not self-hosted and free software, I do not want to use reCpatcha on the registration form. Is it possible to include some other form of self-hosted captcha during the registration process so as to not use Google’s reCaptcha?
Sure it is. This is called an authenticator. Check out the Server Developer Guide https://www.keycloak.org/docs/latest/server_development/index.html#_auth_spi
and you‘ll see there two things: First, you implement your „own“ captcha (I guess that‘s what you want to do) by building a class, package and deploy it on the server. Second, you define the authentication flow, remove the unwanted captcha and add your new one. If your deployment of the first step was successful, you can find your authenticator in the admin ui where you configure the flows.