The Steam bug that corrupted Arma 2 installs when any DLC was active has been fixed in the main/normal branch of the Steam client.
You just need to open Steam and let it update itself (if it hasn't already). After the client updates, your DLC and Arma 2 will start working normally again.
This was the recent Windows 11 / Steam issue that prevented the game from starting or kicked you from servers due to a file-signature mismatch. If you still have trouble, see Troubleshooting or ask in #support.