This hits the nail on the head… what Austria is up to here is more about gamesmanship to make sure A) their interests in Germany are protected and B) to make Francis feel important rather than impotent. And if said gamesmanship chips away at the Franco-Russian detente? All the better.
To quote from the Russian classic of the XIX century “how to turn a losing enterprise into a profitable one without making any changes in it”. Or, as in “An elephant and a pug” (the pug barking at an elephant explains her behavior): “without any fight I can get reputation of being very brave”
I was trying to be nice to the Brits but even in that overly optimistic scenario a practical British help with the troops would be too small and too unreliable to be seriously counted upon by the Austrians (who, after all, are reasonably sane and pragmatic). And a little adventure vs. the Ottomans, especially with the Russian help, is a reasonably low risk war with a distinct possibility to get at least the token but possibly even valuable gains.To say nothing of the fact that the worsening situation in the Spanish Americas for Britain makes landing even a token force in Italy a huge difficulty