How can I test why the API response from Woocommerce is slowing down or timing out?

i’m fairly new to WordPress/Woocommerce, so I need help from you.

One of our sites with Woocommerce has a problem with its REST API, sometimes it loads in 2s, sometimes more than 30s and sometimes it eventually times out.

Is there any way to know what is causing the problem? Any plugin that can help me pin point the point of failure?

What I am planning to do is basically copy the site from production to local and check by disabling plugins one by one. But this could be time consuming and inaccurate because of different environments.

Any help or suggestion is appreciated. Thank you.