Wordpress - Can I use REST-API on plain permalink format?

Yes you can. Just add the rest_route query parameter.

So

https://wordpress.org/wp-json/

would become

https://wordpress.org/?rest_route=/

Or https://wordpress.org/wp-json/wp/v2/ would become https://wordpress.org/?rest_route=/wp/v2 to give you a more complete example.

So you're wondering how to decide which one to use? Worry no more, there's a function for that: get_rest_url()

Another option is the fact that by default there is a <link> in the header that gives you the API root.

<link rel='https://api.w.org/' href='https://wordpress.org/wp-json/' />

So in case you need to figure that out from client side JS just use something along the lines of

document.querySelectorAll('link[rel="https://api.w.org/"]')[0].getAttribute('href');

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So basically you shouldn't take the wp-json part as given (and hardcode it) but always build it dynamically either using get_rest_url() or the JS approach mentioned above.