These are the codes relevant to your question, from NFPA 96 2021 version. You can access the entire code book for free at the NFPA website.
8.2.3.1 A hood exhaust fan (s) shall continue to operate after the extinguishing system has been activated unless the fan shutdown is required by a listed component of the ventilation system or by the design of the extinguishing system.
8.2.3.2* The hood exhaust fan shall start upon actuation of the extinguishing system if the exhaust fan and all cooking equipment served by the fan have been shut down, unless the fan shutdown is required by a listed component of the ventilation system or by the listing of the extinguishing system.
8.2.3.3 The exhaust fan shall be provided with a means so that the fan is activated when any heat-producing cooking appliance under the hood is turned on.
8.3.2 When the fire-extinguishing system activates, makeup air supplied internally to a hood shall be shut off. -- Keep in mind that RTU's may be used for make-up air, and if so, you'll need to shunt the T-stat wire to turn it off.
10.4.1 Upon actuation of any fire-extinguishing system for a cooking operation, all sources of fuel and electric power that produce heat to all equipment protected by the system shall automatically shut off.
10.4.2 Steam supplied from an external source shall not be required to automatically shut off.
10.4.3 Gas appliances not requiring protection but located under the same ventilation equipment where protected appliances are located shall also be automatically shut off upon actuation of the extinguishing system.
10.4.4 Shutoff devices shall required manual resetting prior to fuel or power being restored.
10.4.4.1 Where an electrical gas valve is used for shutting off gas appliances, a manually reset relay shall be used to restore electrical power to the gas valve.
10.4.5 Solid fuel cooking operations shall not be required to be shut down.