Find a reputable local locksmith. Do NOT call a national company or some scammy company that come up on Google Ads.
Tell them the snib fell off your night latch and you would like the door opened and latch replaced. It’s easier if you can let them in a window or back door, but if not they’ll neatly drill through from the outside to release it and then replace everything.
Unfortunately, on a Friday night, it’s likely to set you back £200+, but trust me when I tell you this is the best way. Your picks and tension wrench aren’t going to do shit.
Also, I’ve just noticed the scraping on the latch bolt. Chances are your hinges are bent or incorrectly fitted. If the locksmith points this out and offers to rectify, pay the man. In the long run, it’s worth it.
……..Wow, nobody knows shit in this thread. You need a hook lockpick or a ‘control’ key to depress the back retaining wafer when the cylinder is pushed into the housing, this allows for it go to deeper and have the retaining wafer be locked into the housing, you may have to unlock/lock the device to get the right timing.
It is a wafer lock, we typically call the device a T-handle. Sometimes you might have a retaining wafer, usually this stuff is just sealed at the factory and a replacement is more economical.
The T-handle could be held in place by screws from inside the door, or rivets.