Does any country have regulations that require a certificate or approval of the aircraft that use portable Wi-Fi in flight? Is there an FAA or EASA regulation or advisory, or an ICAO document or advisory?
The FAA touches upon it in this letter
Current FAA regulations require an aircraft operator to determine that radio frequency interference from PEDs is not a flight safety risk before the operator authorizes them for use during certain phases of flight. Even PEDs that do not intentionally transmit signals can emit unintentional radio energy. This energy may affect aircraft safety because the signals can occur at the same frequencies used by the plane’s highly sensitive communications, navigation, flight control and electronic equipment. An airline must show it can prevent potential interference that could pose a safety hazard. The PED ARC report helps the FAA to guide airlines through determining that they can safely allow widespread use of PEDs.
The operator is responsible for determining that the unit does not create any interference they link off to this document which is pretty verbose and outlines a lot of the info you may be looking for on this front.
This document elaborates a bit more on the regulations
Aircraft with an FAA-approved system— such as an Onboard Mobile Telecommunications System (OMTS), Wireless Fidelity (WiFi), airborne access systems (AASs), or Network Control Units (NCUs)—are considered PED-tolerant for PEDs used with the installed system. If an aircraft model has demonstrated tolerance for both transmitting and non-transmitting PEDs, the operator may allow PED use during all phases of flight on this aircraft model.
Aircraft need to be shown to be PED tolerant for Wifi units. You can find an AC covering whats involved in that here.