Can the Graceful trait be used in a session once for the Speed-test and once for Social Skills requiring grace or presence?
Nope, still just one total time per session. You have extra flexibility in what it can be used for, but it is still one call-on trait, and as such can only be invoked once per session.
Are you sure? It mentions the extra cost, but there are other call-ons that specifically say they work with X skill AND Y skill that only cost two points - Glib, as an example, is a Call on for three different skills (Soothing Platitudes, Falsehood, and Seduction) and I can’t find a specific rule stating that a Call-On Trait inherently must only apply to one skill - only that it can be used once per session. As such my read of Graceful was that it can be invoked for each of the two skills once per session, hence the double cost.
You can choose during the session to either apply Graceful to a Speed test or to apply it to a social test requiring grace. The flexibility is the ability to use it in either sphere. But it still obeys the Call-On rule that it may only be used once per session.
Graceful is significantly broader than this. You can use it on pretty much any Speed test and, by my reckoning, about 80% of social tests.
Though I can see how “double-effect” could be read as “use twice”.