Where did you find that Russia opposed France annexing the Netherlands ?
Maybe not as much as as the Dutch, British Austrians and Prussians but they didn't want France getting it. The 3 biggest land powers: Russia, France, Austria feared and mistrusted each other. The Franco-Austro-Russian alliance during the 7YW was fragile and could easily have broken up. Frederick's unprovoked invasion of Saxony angered Austria and Russia (who had wanted parts of Saxony) and brought them closer together. Louis XV's mistress, Pompadour, who was angry at Frederick for insulting her, convinced him to join the alliance.
If Frederick did not invade Saxony, the alliance would have broken up. It might have ended up as Britain/Russia versus France/Prussia with Austria on the sidelines. France might even have Spain onside since France would not be allied with feared Austria. If Spain joined, then Britain would have been likely to drop out entirely.
And Prussia ? Indeed it was France lack of consistency about the Netherlands that persuaded Friederich II to drop his alliance with France.
It was France that broke up the alliance with Prussia, not the other way around. Frederick did think that the French were wimps in not declaring war on Britain after the latter was making aggressive moves on French ships and colonies but that was not enough for Frederick to break up the alliance. In fact, diplomacy leading up to the 7YW was complicated but Frederick at one point was willing to betray Britain to court France. Frederick's invasion of Saxony and Madame de Pompadour pushed France more deeply into Austria's camp.
The Dutch could afford nothing. They risked total annihilation.
The Dutch was still a major player. They had an excellent banking system and would have had Britain, the best naval power, and Prussia, the best land power, as allies. The Dutch was also an important supplier of badly needed naval supplies to France. Antagonizing the Dutch was not in France's best interests. In fact, everyone was surprised that the Dutch remained neutral during the 7YW; when the war started, Britain had sent transports to pick up Dutch troops, figuring that the Dutch would join the war only to be forced to call back the transports when the Dutch told them no. The Dutch were satisfied by France's promises not to attack the Austrian Netherlands and stayed neutral. They even continued to sell naval supplies to the French during the war. Britain objected to this but, like France, still felt it important not to antagonize the Dutch, proving that the Dutch, while in decline, was not yet a minor player.
And the fact is that France not keeping the Netherlands was decisive in Britain's decision to start war anew just 6 years later.
What is it about the Austrian Netherlands that would have prevented Britain from going to war against France? If France had Hanover, (which France planned to capture in the 7YW to exchange for any lost colonies) then that would be a different story.