anotherlife I don’t understand why do you try to divide Ukraine. Odessa is a city of Ukraine and let it be further.
If talking about more ancient history of the territory,
There were greek cities in northern coast of the Black Sea and in Crimea. The name Odessa comes from Odessos - antique port city. [but later ruins of Odessos were found not far from Bulgarian Varna]
Then those steppes were home for different nomad tribes - Pechenegs until 10-11 century until Slavanians got those lands, 12-13 century those lands were under nomad tribes Polovtsy (Kipchaks) until Mongols came.
Mongols also defeated whole Rus’ and planned to move to Europe but lost too many warriors fighting agains Rus’, so they were only in some Polish and Hungarian lands for a pretty short period.
After 3 centuries under Mongols Rus’ was divided into Velikorus’ (Great Rus’ - Moscovian), Malorus’ (southwestern one, including Kiev) and Belorus’ (White Rus’). Polish and Lituanian Principality took lands of Malorussia and Belorussia under their control until 15 century when Rus’ was finally rejoined. But northern coast of the Black Sea was under Ottoman Empire which appeared after Eastern Roman Empire collapsed.
In 17th century Peter the Great moved borders of Russia to Baltic coast thanks to victory over Sweden and to The Black Sea coast. After numerous war conflicts between Russia and Ottoman/Turkey Russia got those territories and that was until 1991.
So if speaking basing on history Odessa region may belong to either Turkey or Russia or Ukraine. All other nations do not exist anymore.
But Turkey lost it in 17th century as well as Crimea.
Russia - Ukraine conflict is a kind of divorce as they are the same nation with the same history.
While Malorussia and Belorussia were under Polish some difference in culture and way of living appeared in those lands comparing to Velikorussia (Russia). Their language switched closer to Polish, catholics appeared and became major confession. Those changes were used later in political aims by Russia’s external enemies who wished to cut Russia into some pieces. National and confessional frictions are still the main instrument for Brits to create problems inside their enemy’s states (India, China, USSR, Yugoslavia, Middle East...)