Figured it out, I was missing some Steam DLLs. Steam now properly initializes. Should’ve payed closer attention to the documentation, as it was spelled out here: Determining required DLLs for Windows game servers - PlayFab | Microsoft Learn.
Using ListDLLs, I discovered that my local server was referencing these dlls on my PC (which were not included with my PlayFab server):
steamclient64.dll
tier0_s64.dll
vstdlib_s64.dll
crashhandler64.dll
I’m guessing only the first two dlls are required as I’ve seen them often referenced with Steam servers, but I added all 4 to the server package regardless. The location I put them in was "<project_name>\Binaries\Win64". I wrongfully assumed these would be wrapped up into the prerequisites when packaging with Unreal. I had to copy them over from my Steam directory (C:\Program Files (x86)\Steam).