Changing the key on the song edit page does not do anything to the song chords - it does not adjust the chords. This is purely used to identify the key of the song (for auto pads, set list info, transpose, etc.).
e.g. if your song is set in the key of E

Changing the key to C# in the song edit window, does not adjust these chords. It will say 'C#' in the set list and if you play the pad, it will play C#, but the chords shown will be in the key of E as before. Say you wanted easier chords to play (e.g. C, F, G), but did want the key lowered from E to C#, what you should do is first transpose the key/chords using the transpose function. This will then make the chords follow the new key. The original key will remain as 'E'. Making sure this is set, means you can use the transpose function to transpose back to this key.

Then, from the capo dropdown, select the value that gives nice chords (e.g. 1 (C)). This leaves the song in C#, but will give the option of showing the capo chords in C.
When you view the song, depending on your preference for the chords, you will either see the native chords only (i.e. in C# despite the capo), the capo chords (in C), or both. Capo chords show in a different colour



You can change the capo chord display preference from Settings > Song actions > Chords >. Chord settings

I tend to have one of the page buttons set to capo toggle (which cycles through these values)
Hope this makes sense?
Gareth