From: Upstate New York USA
1) You said you looked, "some days later." How many days was that? When you switch from Pierside repair to Readiness, it typically takes 3 days before the ship is eligible to sail. If at some point you tried switching it back into Pierside again you may have restarted that clock.
2) Major damage will not repair in readiness mode. I'm not sure if a level 4 port is big enough to repair major damage at all. Someone else can weigh in on that. If it does, the repair process may be slow enough that you didn't notice the damage going down in the period you left it there.
3) You said you saw the "X" showing no repair when it was in Readiness mode. That would be expected, since repair of major damage doesn't happen in readiness mode. What was the symbol or number in that place when the ship was in Pierside mode? That will tell you a lot about your conditions. A number is the estimated days to complete the repair. If the number is large, then see #2 above.
4) When you created a TF for the ship, did you try an Escort TF? These are designed to move any type of ship anytime, including heavily damaged craft. Sometimes if damage is bad enough the game engine will not assign a ship to combat duty such as an ASW or Transport TF. Your damage numbers don't look high enough for that, but again, someone else could tell you better.
If those items don't solve your issue, posting a screen shot of the ship repair screen in both Readiness and Pierside repair mode might be helpful.
"It's all according to how your boogaloo situation stands, you understand."
Formerly known as Colonel Mustard, before I got Slitherine Syndrome.