Let me bring up a few items I know about to support my comment above.

The Haudenosaunee word for "Irondequoit" is "O-nyiu-da-on-da-gwat" which translates to "the lake turns aside". See this link for that info and more information about how early explorers of the area traveled Lake Ontario to Irondequoit Bay looking for a water route to Asia: https://www.hmdb.org/m.asp?m=108625

This Aboriginal Occupation of the Lower Genesee paper, written by George H. Harris, describes the definition or "Irondequoit" in more detail, see page 35 of this document.  https://libraryweb.org/~digitized/books/Aboriginal_Occupation_of_the_Lower_Genesee.pdf

This civil plan for the Management of the Irondequoit Bay Harbor system describes Irondequoit Bay as "One of the largest coastal bays of Lake Ontario..." This resource also describes the Bay as "a major nursery area for the Lake Ontario ecosystem". https://www.monroecounty.gov/files/planning/IBHMP%20Final%20Report.pdf
That pdf can be found with other references here: https://www.monroecounty.gov/irobay

The New York State DEC regulates fishing in the state and indicates that fishing regulations follow those of Lake Ontario, so this waterbody is managed by a Government entity exactly the same as the lake. Source: https://dec.ny.gov/places/irondequoit-bay
