This has been a bug that has been present in the game for almost a year since Season 6, long before we could see our full bridge crews and ships on the character select screen. It's a result of the UI change that allows you to ready both a starship and shuttle at the same time from a shipyard.
When you beam up into space, the code is written to make the game load your shuttle and then your ship. You aren't supposed to see your shuttle appear, but I have seen this happen to me more than a few times since S6. For some reason, this glitch fails to load beyond your shuttle up to your ship. For now, you have to select another character then back to the gitched one for it to show your ship.
This glitch also breaks character info database retrieval when you click on other players in space or on the ground and click on "i" info button next to their portrait. 9 times out of 10 you'll see a mostly blank info window, or it will show the name and class of a shuttle they have ready even if they are clearly piloting their starship.
Season 6 was a heavily buggy addition to STO, but it's simply not profitable for Cryptic to go back through the layers and fix it. Expect this shameful bug to persist for a longtime to come.