I installed WordPress 5.3.2 and using the TwentyTwenty theme for this non profit I joined. I was trying to make a new Page and save but it kept complaining the REST API call failed and the page would not save.
The REST API call gave the following unexpected result: (404) Not Found The requested URL /wp-json/wp/v2/types/post was not found on this server.
Looked at Tools->Heath Check and noticed that I missed some php lib. After installing the libs that did not fix the error either.
You likely changed the Settings -> Permalink
I had changed it to just post. Once I changed it to custom
the API error went away and verified that the heath check passed too.