Please check if your REST API is loading correctly

I run a multisite. On the primary server things seem to be OK. On the subsite harrogateitconsulting.uk I’m seeing a red warning:

“Please check if your REST API is loading correctly. Your site currently is using the slower Ajax fallback method to load the settings.”

I’ve checked the “more info” instructions at https://burst-statistics.com/instructions/rest-api-error/ and I’ve reached the “Please contact us so we can figure out the problem” stage.

FWIW WordPress also thinks my REST API isn’t working properly for this subsite, but I don’t know what it wants so I can’t verify it manually.

I’ve got Apache Rewrite rules like this one, and testing with wget I receive the result you describe in your help document – no errors reported:

RewriteRule ^/wp-json(/.*) /usr/local/app/wordpress/index.php?rest_route=$1 [L]

Unfortunately I really am at a loss at this point. I’m beginning to wonder if multisite was a bad idea, but as I’m running three different sites each on their own domain it seemed to make more sense than replicating everything multiple times.