Hi there,
I tried changing the Permalinks setting to the default value (first option) and it seemed to fix the issue.
I changed it back to the value you had added.
Strangely, it wasn’t working with the normal “Postname” option, either.
This tells me something is up with the mod_rewrite module on your server. When permalinks are being altered, it’s breaking the REST API.
I would report this to your hosting so they’re able to debug internally.