Re: "Screen share microphone problem : they can’t hear me"
You may want to check:
(1) the settings for "mute" on / off are working ok in FaceTime
Eg: Change audio options for FaceTime calls on Mac - Apple Support
(2) the microphone is not in use for another app / or for what you are sharing.
(3) Your iOS 26 version is up-to-date with the latest version:
(You can check in Settings > General > Software updates)
Also see:
Choose a camera or microphone for FaceTime calls on Mac - Apple Support
________________________________________________
Re: "... trying to figure out the problem and the solution"
Find the cause, and you likely have the solution.
Useful resource : FaceTime User Guide for Mac - Apple Support