PS5 Controller randomly turns off and doesn't reconnect to steam

[Kensworth]

I have a PS5 controller that I use to play certain games on Steam with. I can use the controller in Bluetooth mode for a little while but then it will randomly turn off and when I turn it back on it would not connect back to Steam just to my PC. I know that this is happening because I changed the LED color to purple when it is connected to Steam when it is just connected to my PC and nothing else it has the basic blue color. I have to connect it back to my PC through a wired connection for it to connect back to Steam but if I disconnect the wire and try to use it back in Bluetooth mode it loses the connection to Steam again. I had noticed that when I disconnected the wire from my headset to plug that cable into the PS5 controller for a wired connection (both my headset and PS5 controller use a USB type C cable) when my headset switched to Bluetooth mode the controller reconnected back to steam for a bit but then it lost connection again. Does anyone else have this problem or a solution?

My headset is corsair virtuoso.