Tactical repair does repair damage every phase of combat. It's always worked that way, and is one of the primary reasons to use ancient civs. With the ancient research boost already nerfed, removing living ships would make ancient mush less desirable for players to use.
I don't want "Living ships" to be removed ) It's a cool concept. But just to provide context - at about turn 100 the most powerful civ in the galaxy declares war on me (because, you know, i'm "ripe for conquest") and my military is like 4 times smaller than theirs. But due to having living ships and several good fleets consisting primarily of cruisers I managed to defeat all their fleets and conquer all their planets in about ~15 turns. Sustain in battle is just insane. Just like on the 1st screenshot, that commander battleship repaired almost the value of its total hp. Reminds of my old days in eve online, when you could fit your ship with active repair and energy modules properly and it was nearly impossible to outdamage its self-repair without considerable firepower. During that whole war I lost maybe 2-3 cruisers and some frigates here and there. If anything, perhaps it should be slightly nerfed. Right now, ancient seems to be the strongest trait with living ships (which also remove ship upkeep) and insanely good precursor protection field module. Of course it should be very strong, because hell, they are almost precursor civs themeselves.
Anyway, balance matters aside, I think it's a visual bug - the game just doesn't update hp value taking into account tactical repair and the health bar of the ship. But "repair" value seems to be updating.
