When you beam in and clip the transporter wall, if you look down, wasn't there already a shuttlebay there?
As for the "Take shuttle to Fleet Starbase" text fix... don't count on it. Klingons exiting from Sirius Sector block still get a popup saying they're cleared to enter Sirius Sector block.
And on Transwarp... There is a transwarp gate in orbit of New Romulus. Why doesn't that thing do anything? Would've made sense if they'd attached its use to the T5 reputation. Tray transwarp power and/or fly upto for a quick connection to your faction homeworld. (Though I suppose that would've devalued the shuttle ride a little.)
"Don't let them promote you. Don't let them transfer you. Don't let them do anything that takes you off the bridge of that ship, because while you're there... you can make a difference." - James T. Kirk
I think it best not to overthink the feature too much; I doubt you're taking a shuttle straight to the fleet starbase (or vice versa) but rather to your ship which then goes with you.
It could definitely do with some tidying up to make more sense, and a special loading screen would be nice, but it's just a fast travel system after all. I expect if we get any additional fleet holdings in the future that they'll also have shuttle access added for convenience so you can hop between the different fleet stores and mini-missions.
It works, I guess, like the TW to Fleet Starbase. You TW there from wherever you were. Say, DS9. You do your business, you beam back to the ship, then warp back to sector. Are you in Eta Eridani? No, you're at DS9 again. While this doesn't seem to make sense, it does allow you to quickly pop over to your base and do what you need to do, without requiring you to hike back to where you were.
I do agree that it would've been better handled by the Transwarp gate, but maybe there was a technical issue with tying an ability for the TW gate (part of the Starbase holding) to progress on the Embassy holding?