[rest] What’s the best RESTful method to return total number of items in an object?

As of "X-"-Prefix was deprecated. (see: https://tools.ietf.org/html/rfc6648)

We found the "Accept-Ranges" as being the best bet to map the pagination ranging: https://tools.ietf.org/html/rfc7233#section-2.3 As the "Range Units" may either be "bytes" or "token". Both do not represent a custom data type. (see: https://tools.ietf.org/html/rfc7233#section-4.2) Still, it is stated that

HTTP/1.1 implementations MAY ignore ranges specified using other units.

Which indicates: using custom Range Units is not against the protocol, but it MAY be ignored.

This way, we would have to set the Accept-Ranges to "members" or whatever ranged unit type, we'd expect. And in addition, also set the Content-Range to the current range. (see: https://www.w3.org/Protocols/rfc2616/rfc2616-sec3.html#sec3.12)

Either way, I would stick to the recommendation of RFC7233 (https://tools.ietf.org/html/rfc7233#page-8) to send a 206 instead of 200:

If all of the preconditions are true, the server supports the Range
header field for the target resource, and the specified range(s) are
valid and satisfiable (as defined in Section 2.1), the server SHOULD
send a 206 (Partial Content) response with a payload containing one
or more partial representations that correspond to the satisfiable
ranges requested, as defined in Section 4.

So, as a result, we would have the following HTTP header fields:

For Partial Content:

206 Partial Content
Accept-Ranges: members
Content-Range: members 0-20/100

For full Content:

200 OK
Accept-Ranges: members
Content-Range: members 0-20/20