Seems I got it working with 8.2.2 and 25.0.2 with the changes (without the /public) above 
I get the ‘x Connected as Administrator’ window now.
Info for others, in case you need to change the ID and secret, like me because I thought I had the false password-type: It’s in nextcloud-DB hidden not in a table with ‘integration_suitecrm’, but in ‘oc_appconfig’ and ‘secret’ is in plain text (sic!).
Don’t know if the integration does any useful and it’s bad that it’s so stupid not to change ID and secret easier (the app lets you not switch to former windows-fields). I’m thinking to fork and add own extensions.
Also I’m new to this, so not sure all is propper working now. 