Hey, there
Found some others around this with other games as well. Here is what I found that may help you out.
Fix 1: Disable the EA App Overlay (Primary Cause)
Even if you own and play the game through Steam, the EA App runs silently in the background and hooks its own overlay into the game, causing severe input locking and micro-stutters.
Open the EA App on your desktop.
Click your profile icon in the top-right corner and select Settings.
Go to the Application tab.
Scroll down to In-game overlay and toggle it OFF.
Fully restart Steam and launch the game.
Fix 2: Rebind or Change the Screenshot Key
F12 can conflict with function key layers or in-game bindings. Rebinding it clears stuck hotkey handles:
In Steam, go to Settings > In-Game.
Find Screenshot shortcut keys.
Change it from F12 to a key far away from standard game inputs, such as F8, Pause/Break, or Numpad Asterisk (*).
Fix 3: Turn Off "HDR Screenshots" / Steam Overlay Notifications
If you are playing with HDR enabled in Battlefield 6, Steam attempts to render two versions of a screenshot (SDR and tonemapped HDR). When the overlay hitches, this thread can loop endlessly:
Open Steam Settings > In-Game.
Turn OFF "Save an uncompressed copy" if it is checked.
Turn OFF "Display a notification" for screenshots (the notification pop-up itself often causes the overlay thread to crash and loop).