The end of day logs are generated in a specific order with work coming first and escape attempts happening later. There isn't much that correlates between the two. Low obedience is a requirement to escape but not a requirement to work. The only odd part is that Ayneris should be acquired with relatively high obedience, so escape shouldn't normally occur on the first day unless you have some significant problems.
Normally when a slave escapes they are deleted from the game data so there is no hope of recovery. However, from your second screenshot you appear to be playing with Aric's mod, which includes semi-persistent data for NPCs. So for a little while after escaping she should be present in outskirts of your home town. It's a complex system so it's hard to say what your chances of encountering her are. The mod will not keep infinite NPCs on file and with each additional person generated for random encounters the chances of her getting purged from the file increase, also her data will be updated after each day so she may move to nearby areas. I believe there is an auction/execution event that occurs in the town center when the mod purges NPCs.
Otherwise it's quite easy to edit the save file to reset her quests and acquire a new Ayneris.