Media is not available via rest-api while Posts etc. is…

HI, I just started to integrate the Rest-API into our internal CRM system in order to post and update certain custom post types on our website. Trying to do so with “Posts” and CPTs works fine.

I use CURL-commands in our CRM-database to connect with the website and use

But when I try to access “Media” the access seems restricted, see here:

{
    "code": "rest_upload_no_data",
    "message": "Keine Daten bereitgestellt.",
    "data": {
        "status": 400
    }
}

I am not aware to have this set manually, can cannot find any rule or parameter in wp-config.php or .htaccess and I believe not to have any plugin running that alters the default setting (well, you never know).

Any idea how I can “open” the Rest-API for “Media”?

And while I am already asking: Can I block normal users from the web to read/see the Rest-Api while my CRM system can do access it?

Kind regards, Martin