I have a hose reel where this one piece has broken.
I literally can not come to spend another $100 on the entire assembly when all that's broken is this piece, but I don't even know what to search for in this case.
Our big-box stores definitely don't carry it.
It allows the assembly to spin (for reeling in, and unreeling)...
This is where it goes:
A swivel or "rotary union" (but there are many things under the same names that don't look like that, or in some cases work like that. It's imprecise, but does cover what you have, as well as some other things.)
Specifically one with one side "garden hose thread" and the other appears likely to be pipe thread in a smaller size.
My strong suggestion is that you contact the manufacturer of the hose reel unit. It is possible that the part that broke in yours is a custom part for that manufacturer or a specialty product that is typically only available in large quantities to hose reel manufacturers.
I have had parts go bad in things in the past and found that gentle and patient communications with the manufacturer have led to them sending me replacement parts for nominal cost if not for free.
Parts can be found. A quick look at Amazon shows this part which may be adaptable to your model reel. https://www.amazon.com/Liberty-Garden-Products-4009-Replacement/dp/B07ZWT6NBX/ref=sr_1_14?dchild=1&keywords=water+hose+swivel&qid=1611207801&sr=8-14
