If you've already restarted your router, check your TV settings to see whether AirPlay is enabled. Go to Settings > Apple AirPlay and HomeKit, and make sure the toggle is set to On.
By the way, what kind of TV do you have? Not all Sony TVs support AirPlay 2. Newer models do, but many older ones don’t.
You can also use a wired connection, which always works reliably.
You need a Lightning Digital AV Adapter (by Apple) and an HDMI cable. Connect the adapter to your iPhone, plug one end of the HDMI cable into the adapter, and the other into your Sony TV. Then switch the TV to the correct HDMI input, and your iPhone screen will appear instantly.
If you don’t like using a cable, consider using screen mirroring apps. There are plenty of them in the App Store, just search for mirror apps or something similar.