public support = open support?

Yes. Open non-concealed (therefore, public) information.

Russia has a "public" face, one they want the world to perceive as the real thing. It may show one leaning, while in the background, some very different actions may be taking place.

Politicians and Actors may have "public faces" because they are on-stage at all times. Countries also have a "public" face.

Russia's public support of the Serbs does not necessarily mean "open support," because it is not certain that Russia would intervene on behalf of the Serbs if, for example, NATO again attacked Serbia militarily. The Russians did not attempt to intervene when NATO attacked Serbia in the Kosovo affair. Russian long maintained a position of "supporting" other Slavic peoples as in opposition to Turkish claims in the Balkans. In 1877-78, the Russians defeated the Turks in a Balkan war, and handed over lands which Turkey had claimed in what to the principality of Bulgaria--in particular, that portion of the Balkans known as Macedonia. Otto von Bismarck convened the Congress of Berlin in 1878, and to balance the claims of the British, the Austro-Hungaria Dual Monarchy and Russia, while preserving the Turkish Empire, certain of the lands, especially Macedonia, were handed back to the Turks. Russia's excuse to go to war with Turkey was their "support" of the "Little Slav Brothers" in the Balkans--the Bulgarians, the Serbs, the Montenegrins and the Romanians. In the face of German opposition, the Russians backed down.

It is difficult to answer this question without knowing what you mean by "open support." Russian will rattle its saber and make dire warnings about what it will or will not tolerate with regard to the Serbs, or other Slavic states--but they have not attempted to intervene in the Balkan wars of the late 20th century, so what the support is actually worth is anyone's guess.