Why don't my bathroom outlets work after an appliance power surge?
Having a circuit failure when using a portable heater is probably the number one cause of receptacles not working.
In the U.S. The most common cause is use of back stabs (push in wire connectors). After that loose wirenuts then a loose or broken wire or wire in the service panel.
Your receptacles show hot but what about the return or neutral? If this connection is damaged the circuit won’t work but will show hot with a non contact tester.
If you work towards the service panel on this circuit the last working receptacle or switch or the first non working one will be where the failure is. Use a light or hair dryer to see which outlet it is. Turn off the power and look in this case for a loose, burned off or broken white wire, if things look good with back stabs and things start working when you turn the power back on the circuit will probably fail again when under heavy load so if you find backstabs it is best to move those connections to the screw terminals or if no terminals buy a receptacle that has them, 99c specials work 3-5$ specification grade are worth the extra and will last longer and hold the plug better.