WPCOM_REST_API_Proxy_Request_Trait: Move to connection from the JP plugin

[manzoorwanijk]

Move the WPCOM_REST_API_Proxy_Request_Trait from the Jetpack plugin to the Connection package so it can be used by standalone plugins.

Related Slack discussion: p1736318126270229-slack-C05PV073SG3

Improvements to consider when moving the trait:

• Add an option to override $request_options to allow passing additional options like timeout. See 762b860

[github-actions]

OpenAI suggested the following labels for this issue:

• [Feature Group] Other Infrastructure: This issue relates to moving a trait between plugins, which involves underlying infrastructure changes.
• [Feature] Jetpack: The WPCOM_REST_API_Proxy_Request_Trait is originally part of the Jetpack plugin, which is directly impacted by this change.
• [Feature] WP REST API: Since the trait in question is related to REST API requests, this label is relevant as it indicates the functionality being discussed.

[github-actions]

This issue could use some more labels, to help prioritize and categorize our work. Could you please add at least a [Type], a [Feature], and a [Pri] label?