My first thought when I read your post was bobcat. You said it killed many. A bobcat can kill many and will keep coming back to collect the bodies until it removes them all. A bobcat can climb, which you mentioned, and fit though a much smaller opening than you'd expect. The print you posted a picture of looks like a can print. The gap above the door you posted a picture of is big enough for a cat to get in. Regardless of what it is, you now have to try and catch it in the act, as in trap it or lie in wait near the coop and hope your scent doesn't deter it. Cats (and weasels) are both quite clever, good climbers, good killers, and will return, however they both can know enough to avoid traps and avoid people. This is no easy task.
As others have mentioned, before your remaining birds go back in the coop, you may have some fortifications to do. One area of opportunity I saw is along your roof line. You appear to have corrugated roofing, and the gaps this creates are large enough for many small rodents/weasels/snakes/etc. If you are counting on these gaps for ventilation, you can cover them with wire fencing of some sort, but if they are not needed for ventilation, you can look into these, which fill the gaps...
https://www.lowes.com/pd/Tuftex-5-P...ylene-Solid-Roof-Panel-Closure-Strips/3048079
Good luck! You've got a difficult mission ahead of you and I hope it turns out favorably.
As others have mentioned, before your remaining birds go back in the coop, you may have some fortifications to do. One area of opportunity I saw is along your roof line. You appear to have corrugated roofing, and the gaps this creates are large enough for many small rodents/weasels/snakes/etc. If you are counting on these gaps for ventilation, you can cover them with wire fencing of some sort, but if they are not needed for ventilation, you can look into these, which fill the gaps...
https://www.lowes.com/pd/Tuftex-5-P...ylene-Solid-Roof-Panel-Closure-Strips/3048079
Good luck! You've got a difficult mission ahead of you and I hope it turns out favorably.