Connection: review the use of the HTTP_RAW_POST_DATA global

The `HTTP_RAW_POST_DATA` global [has been deprecated](https://github.com/Automattic/jetpack/issues/16488). We're using it to [set](https://github.com/Automattic/jetpack/blob/master/projects/packages/connection/src/class-manager.php#L2431) the `Manager::raw_post_data` property in `Manager::xmlrpc_methods`.

We should review the use of `HTTP_RAW_POST_DATA` and the `Manager::raw_post_data` property in the `Manager` class. For example, `$this->raw_post_data` is passed to the `jetpack_signature_check_token` filter hooks. Will this work properly if the `HTTP_RAW_POST_DATA` global is not populated?

Start in projects/packages/connection/src/class-manager.php at the Manager::xmlrpc_methods code that sets Manager::raw_post_data from HTTP_RAW_POST_DATA. Trace how raw_post_data reaches the jetpack_signature_check_token filter hooks and determine the expected behavior when the global is absent; done means the deprecated global's use and filter behavior have been reviewed and addressed.

Written by the indexing model from the issue text.