I would try to see if the site has any error logs. Perhaps something is having an issue causing the REST API to not be responsive.
If there are no errors then it may not be the site but with your web host. Your web host may be skimping on how much speed they are giving you, making it almost impossible to reduce WordPress server response time for your website.
There is also the possibility that you have to many plugins running which loads on every REST API request. This is just how WordPress functions.
There is a benchmark plugin you can try to reduce what loads per request but must be installed as a must-use plugin.
Thank you, Sir Sébastien. Please let me know if you find any errors
@einsthony I think you are confused with my response. You need to look up for any errors on your site. I don’t have access to it.
Closing topic due to inactivity.