To make an already sticky discussion even stickier, consider this:
It used to be common in some states for dealers to title leftover previous-year's new cars as the new year's. So if they had a few '59s left over when the '60 models arrived, those leftover '59s often were titled as 1960 models. I'm not joking. This had nothing to do with the vehicle manufacturer, but was just another shady dealer practice. This nonsense went on well into the 1970s.
I'd assume changes in safety and emissions laws from one year to the next eventually caused some dealers to get in trouble, which ended the practice. If you say that 1973 car is actually a '74, then you're saying it meets the '74 regulations, and if it doesn't... You get the idea.
The reason I mention this is that you might still run into older cars with a title "off" by one year. In other words, it's obviously a 1969 Mustang, but the title says 1970. Now you know how that happened.
About half-year designations, I don't know of any state with provision for them. As mentioned, the "1964-1/2" Mustang was titled either as a 1964 or a 1965 in every state.
The previous comments tying a model year to January of that calendar year are correct. IIRC you can call a car a 2023 model in the US if it meets 2023 regulations and was produced between 2 January 2022 (the year before) and 31 December 2023. Production on 1 January 2023 has to be MY2023. It can no longer be 2022, and MY2024 production cannot begin until the next day.