"The Avatar State is a defense mechanism, designed to empower you with the skills and knowledge of all the past Avatars." On screen we've only ever seen the avatar state used for bending related purposes but does it also transfer more mundane skills? Say Aang needed to put up a shelf but had never touched a screw in his life could he quickly enter the avatar state and draw upon all the D.I.Y. knowledge of all the avatars and assemble said shelf? (Ignoring the almost sacreligious nature of doing so)
Unclear, but also yes.
We never see Aang doing much besides bending whenever he's in the Avatar State. However, if your question is whether he has any kind of access to the knowledge of his past lives, the answer is a definite "yes". There are multiple instances of Aang accessing knowledge from his past lives that he himself didn't have.
Could possibly have involved the Avatar State:
Channeling Avatar Roku in Jeong-Jeong's tent, during which Aang-Roku states "I have mastered the elements a thousand times over a thousand lifetimes." Note that Aang seemed to have no memory of the exchange afterward.
Channeling Avatar Kyoshi in Chin Village, during which Aang-Kyoshi admits "I killed Chin the Conqueror." Note that Aang definitely had no memory of the exchange afterward.
Didn't involved the Avatar State, but would be a better way of building that shelf anyway:
Learning from Avatar Roku the details of his history with Fire Lord Sozin
Learning from Avatar Kuruk the details (well, some of them) of his history with Ko
Identifying the statue of Avatar Roku at the Southern Air Temple, before admitting "I'm not sure [how I know]-- I just know it somehow."
...or really just asking anyone in the Spirit World if they know
One mundane use of the Avatar State in Legend of Korra is when Korra uses the Avatar State purely to intimidate Baatar, Jr. tied to a chair and helpless to resist. She's obviously not going to bend anything, but her eyes glow and she's able to lift Baatar, Jr.- a fully grown adult- into the air with one arm. Perhaps Korra is just that strong, but I think it's implied the Avatar State provides that strength.
Given that this occurred after the connection to the past lives was lost, I don't think she was using past embodied knowledge- say leverage- to perform this feat.
This acts as a counter-factual example to heightened feats while the connection was in-place. We could say those were all examples past lives acting out and through the present Avatar, but Korra shows the State provides a boost irrespective of that continuity of connection... so we can't be sure that all past examples of the Avatar State involve any kind of skill transfer whether mundane or otherwise. The fact that every Avatar has to undergo training and relearn the elements (and spirit; Korra learns from Unalaq not Aang; Aang learns from Zuko not Sozin; etc) suggests that skill transfer across Avatars is a much more limited thing.