First, check that the jack is free of debris. I'd use a can of compressed air, and 90% isopropyl alcohol to clean out the inside. I'd also attempt to [link|https://www.playstation.com/en-us/support/hardware/dualsense-controller-support/#update|check that controller's firmware is updated], and if the issue persists, then attempt to [link|https://www.playstation.com/en-us/support/hardware/troubleshoot-dualsense/#:~:text=Turn%20off%20your%20PS5%20console,for%20roughly%203–5%20seconds.|re-sync or even reset the controller|new_window=true].
If all else fails, then the issue is definitely caused by physical damage. If this does end up being the case, then you do have options for a repair. The first is [guide|142487|replacing the controllers motherboard] since the jack is soldered directly to the main board. The second is using a soldering iron to replace the jack with a [link|https://www.amazon.com/Replacement-Headphone-Jack-Socket-Playstation-5/dp/B096TP2DCQ|new one], which will rely on you having [[Topic:Soldering|soldering skills]], and requires a soldering iron.
Best of luck to you!