So Mutants and Masterminds has something a bit weird in terms of what "Projected" means in the game. Extra Limbs specifically has the following text referencing limbs that confuses me a bit as to what its intent is.
Projection: Your Extra Limbs are merely a projection of your power rather than an extension of your body. There- fore, any harm directed specifically against your Extra Limb(s) has no effect. So, for example, one of your addi- tional limbs could reach into a container of acid or a blast furnace to pull out an object without any harm to you. The GM may require Extra Limbs with this extra to modify their duration to continuous or sustained, but this is not essen- tial. It’s likely Extra Limbs with this extra are not eligible for the Innate modifier. +1 cost per rank. (pg. 160)
Notably Movement also talks on the subjected of projections with Movement: Swinging, which makes me think that the projections are still physical objects.
You can swing through the air at your normal ground speed rank, using a swing-line you provide or available lines and projections (tree limbs, flagpoles, vines, telephone and power-lines, etc.). (pg. 172)
While it costs +1 per rank, it doesn't seem to have any meaningful use unless paired with Elongated Limbs where you can stretch them out beyond your own space. My only thought is that you can use it as Cover to not only be a circumstantial bonus to grabs but also defenses, but if not that what else could this extra do for you?