In your Settings > Permalinks i see you have HTTAccess rewrite rules ie.
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteRule .* - [E=HTTP_AUTHORIZATION:%{HTTP:Authorization}]
RewriteBase /
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
Do you know where that came from? As i believe it stopping the REST API from loading.
If you go to Tools > Site Health you will see this: The REST API did not behave correctly