The 30 to 45 days is almost certainly the formal review clock only, meaning the window that starts once the city deems your application complete. What the website does not say is how long it takes to get to that acceptance point, which involves submitting, getting a deficiency notice, revising, resubmitting, and sometimes repeating that cycle two or three times before the clock officially starts. The six months your contacts quoted is probably a more honest picture of the full elapsed time from first submission to final determination, and that is before any appeals or engineering revision rounds triggered by reviewer comments.
The assumption doing the most work in your planning is whether the lot is even serviceable from the existing mains. Utility extension review scope and complexity varies a lot depending on whether the main is adjacent and adequately sized, or whether you would need to extend it a meaningful distance. If the nearest water or sewer main is undersized or set back from the lot, you may be looking at a capital contribution requirement or a cost-to-extend calculation that changes the economics entirely. That is a separate track from the review timeline and often surfaces mid-process.
The risk you have not mentioned: a lot split behind an existing duplex in a mid-size Ohio city may trigger a separate platting process on top of utility review. Those two tracks do not always run concurrently, and the platting step can add another review cycle with its own clock. Confirm with the city planning office whether an administrative lot split is available or whether a full subdivision plat is required. That distinction probably matters more to your timeline than the utility review window alone.
Before you model anything, I would call the city's engineering or public works department directly and ask them for the average time from initial submission to completeness determination, separate from the formal review period. Ask for a recent comparable project if they will share one.
What does the current zoning allow on that rear lot as a standalone parcel?