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.