Thanks as usual to William for the great reply!

When a piece of music is in a key that means it is primarily using notes from that scale.

Example: "This song is in the key of C major".  Meaning:  the melody (riffs, licks, etc.) and chords in this song use notes from the C major scale.  That is what a key signature is.  Where is it?  Everywhere on the guitar you can play that scale.

If you've learned the song by learning the chords used, the chord progression and the strumming or picking rhythm, then you don't necessarily need to know anything about the key signature.  The key is already contained in the info you are using (the chords & progression).  Mentioning the key is more about conceptually identifying what is going on, but not necessary to know.

On the other hand, if you are jamming with people & are expected to improvise a melody (take a solo!), then you will need to know some scale patterns and how to make musical phrases with them.

In this case, you would need to know: the location of the note C on the guitar fretboard, the C major scale pattern, and how to make some music with the scale.

You don't have to know the entire fretboard.  But you are going to be limited to only using the area with which you are familiar.  If you only know the open C major scale position, that's fine.  Start with that!  And then work on learning more of the scale in a different fretboard location to expand your skill set.

You might find my tutorials on improvisation helpful.  The first one starts simple with the basics & includes a lesson on identifying the key signature.

https://www.guitartricks.com/collection/learning-to-improvise

Hope that helps!