Must a document have legal significance in order to be considered 'forged'?

Yes. In order to be deemed a forgery, the writing must have some legal significance, and it must pretend to be something it is not. For example, it is considered forgery to write yourself a letter of reference for a job and purport it to be from a former employer. The legal liability the former employer could be held to for recommending someone makes it legally significant.

It is not considered forgery to write yourself a letter of introduction to a country club and purport it to be from a former member, because a letter of introduction has no legal, only social, significance. Painting a picture yourself and signing Picasso’s name is legally not forgery, as the painting has no legal significance, unless and until it is offered for sale or security as a genuine Picasso.