I use a different password manager for most sites, but there is one site it doesn't work correctly on, but Safari/Keychain does work. I can manually store my password in Keychain for that one site, and it works correctly. However, turning on password autofill makes Safari prompt to save passwords on all sites, which I don't want. Is there any way to tell Safari to autofill passwords that it knows about but not to prompt to save any new ones?
I'm not sure if this workaround will suit you, but does the site in question offer a "Remember me" type option? If so, you could just manually log into that site and tick the 'remember me' option so that you don't need to log in again.
Assuming the above works for you, then you can keep using your password manager as you do now and also avoid enabling Safari's password autofill function. You can then keep this workaround in place until your password manager supports the site in question.