It's complicated. Russia is not part of that convention, as can be seen on the dedicated wiki page [1], but since the occupation of the Snakes Island by the Russians earlier during the war the "exit area" just outside Danube's Delta is, de facto, controlled by the Russian Navy (barring an Ukrainian cruise-missile or two).
I'm Romanian, I live in Romania (Bucharest), so as I'm geographically close to this I've been following this particular Danube issue closer than the others, but the thing is that the situation on the ground is still pretty muddled. For example, just as the war started the Romanian authorities had suspended commercial navigation on the Chilia Danube Delta Branch, the one on which the Romanian-Ukrainian border is situated, for fear of Russian bombs. Presumably the navigation has been allowed to resume, but nothing official has been made public in the Romanian mainstream press, the only related news was something about the Ukrainian authorities being unhappy with us (Romanians) asking for navigation-related customs taxes that were seen as too high, so I assumed that commercial navigation had, in fact, resumed.
There was also our prime-minister meeting with the Bulgarian side (with which we share hundreds of kms of the Danube) and making a statement afterwards about how the Danube should be made easier to navigate (i.e. a strong hint made to the European Union to send us money to do that). If that indeed were to happen (i.e. if the Danube would be made easier to navigate) then the Ukrainians would be able to send a large part of their exports to Central and even Western Europe (via the Danube-Mainz-Rhine canal) via fluvial ships, at a fraction of the cost they now have to pay doing that using rail and road-transport. That's why (among other things) the Russians have set their eyes so strongly on the Budjak region (i.e. the Ukrainian region just North of the Danube's Delta) and that's why they have bombarded this bridge [2] that leads to that region at least three times in the last few weeks.
