I'd like to imagine that there's a division in Starfleet designed just for weird starship retrieval that has to be common in such a chaotic galaxy.
"Stardate 73012. We are en route to salvage the USS Dakota from the belly of a giant illusion-inducing space whale."
"Stardate 69238.7. We have suffered major hull damage and lost many good lives today. Nevertheless, we were successful in towing the USS Statesman from a black hole that induced vastly accelerated aging due to time dilation."
"Stardate 87461.8. Our mission to stabilize a gateway and salvage the USS Mucinex from Fluidic Space was a success, but my god, THIS SHIT IS EVERYWHERE."
"Stardate 41800.2. While we will continue our search, reports of a Starship Lollipop seem to have been a rumor at best, a complete lie at worst."
Bonus Kelvinverse edition: "Hey, remember the USS Franklin? How she was reported lost a hundred years ago? Get this, we just pulled her out of the middle of a state-of-the-art space station."
Kelvinverse Klingon edition: "We have discovered a massive mining vessel of Romulan origin. The crew says they are from the future. And from another timeline. The paperwork would be terrible, if we were Starfleet. Thankfully, we are Klingons, and we'll just put them on Rura Penthe."