Currently the traffic for MW REST API (/w/rest.php) is routed to appserver MW cluster, the same one as used for page views. REST API is API, so the traffic should be routed to api_appserver cluster.
Tutum, now it seems to work:
curl -i https://en.wikipedia.org/w/rest.php/v1/page/Main_Page/bare | grep server server: mw1374.eqiad.wmnet
Which is in api_appserver cluster. Thanks to everyone involved for a quick turnaround.