So, the book doesn't go too wildly deeply into the nuances of ranks and responsibilities in the Union Naval Department, but we do know that the highest ranking Union officer in the Dawnline Shore is a Vice Admiral Noe Estienne (and that she is sick of Harrison and Karrakis' bullshit).
Otherwise, as far as I can tell, it does seem that Line Commander and then Fleet Commander are ranks of, like, recognition and competence rather than a change in duties, if that makes sense. They don't seem to involve getting "promoted out of the job," unlike an Admiralty, for example.
The book talks about Commander being the minimum to lead a battlegroup, and multiple battlegroups form an ad hoc fleet, and the entirety of battlegroups in a specific theater are a formally designated fleet, and that fleet is under the command of an admiral. It doesn't seem, as far as I can find, that Line or Fleet Commanders have unique or exclusive duties -- it seems like they are still responsible for their own specific battlegroup, because there aren't any other layers between that and fleet from what I can tell.
Most likely, Line and Fleet Commanders are responsible when their ad hoc fleet contains a mix of Commander ranks, I would assume! And I could see a Commander receiving, like, "the provisional rank of Line Commander" for the duration of a deployment if a chain of command needed to be established.
This is all a very long way of saying that, yeah, there is probably a Line or Fleet Commander somewhere in the Dawnline Shore with y'all!
Also, honestly, it probably means it's fine if you guys want to imagine your PC has a promotion or two under their belt.