Does "search your phone" include any externally-hosted content that can be accessed by said phone?

Yes of course. Basically they have ruled the entire warrant requirement for searches and prohibition on unreasonable searches and seizures is suspended within 100 miles of any border or international airport (which is most of the US).

https://www.cbp.gov/sites/default/files/2026-01/cbp_directiv...

3.2 Electronic Device: Any device that may contain information in an electronic or digital form, such as computers, tablets, disks, drives, tapes, flash drives, SIM cards, global positioning systems, unmanned aircraft systems, vehicle infotainment systems, smart watches, mobile phones and other communication devices, cameras, music and other media players.

3.3 Basic Search: Any border search of an electronic device that does not qualify as an advanced search as described in section 3.4, in which an officer conducts a review or analysis of information residing in electronic or digital form on the device. A basic search may include documenting information observed on the device during the search that relates to immigration, customs, or other law enforcement actions in CBP systems.

3.4 Advanced Search: An advanced search is any search in which an officer connects equipment, wired or wireless, to copy and/or analyze the contents of an electronic device. Use of external equipment (including a CBP standalone computer) merely to make the contents of the device available for inspection (including, for example, to bypass a password, overcome encryption, translate content, view files contained in an external drive or other electronic device lacking a screen, or charge a device) does not constitute an advanced search. Documenting notes and observations, as noted in section 3.3, does not constitute an advanced search.

5.1.4 An officer may perform an advanced search of an electronic device only in instances in which there is reasonable suspicion of activity in violation of the laws enforced or administered by CBP or, in the absence of individualized reasonable suspicion when there is a national security concern. All advanced searches require supervisory approval at the Grade 14 level or higher (or a manager with comparable responsibilities). In cases where the inspecting officer and approving supervisor rely on the presence of a national security concern, without reasonable suspicion, to conduct an advanced search, approval from the Director, Field Operations; Chief Patrol Agent; Director, Air Operations; Director, Marine Operations; Special Agent in Charge; or their delegate, is required prior to conducting the search. In compelling circumstances where operational considerations prevent prior approval, notification shall be made as soon as possible. Notification must include an explanation of the national security concern, the compelling circumstances that precluded prior approval, the relevant facts and information supporting the search, and the results of the search.

5.1.5 All searches of electronic devices will be documented in appropriate CBP systems. Officers will document any supervisory approvals required under this Directive and, in the case of an advanced search, the factors establishing reasonable suspicion of a violation of a law enforced or administered by CBP or a national security concern, as well as relevant observations, impressions, and actions taken, as appropriate.

5.1.6 Searches of electronic devices should be conducted in the presence of the individual whose information is being examined unless there are national security, law enforcement, officer safety, or other operational considerations that make it inappropriate to permit the individual to remain present. Permitting an individual to remain present during a search does not necessarily mean that the individual shall observe the search itself. If permitting an individual to observe the search could reveal law enforcement techniques or potentially compromise other operational considerations, the individual will not be permitted to observe the search itself"