I tried replicating the signs by doing a setblock sign which has a translation string, but I am unable to edit that side of the sign on both creative and survival. So what did you change to make it editable?

Hm that is weird. I remember having had the same issue when I experimented around with signs for the first time, but now I am unable to recreate that. Do you have another mod installed, that might mess with signs?

No.

1. Create a vanilla 1.20.4 instance
2. Create a new world
3. Run /setblock ~ ~ ~ oak_sign{front_text:{messages:['{"translate":"gui.cancel"}','{"text":""}','{"text":""}','{"text":""}']}} replace
4. Try editing that side of the sign in survival or creative.

Maybe your test world is older than 1.20, where this bug was supposed to be fixed?

Signs with non-text chat components can no longer be edited

Oh, turns out you need to have a static text component on the same line as the keybind, or translatable as well. So your command would look like
/setblock ~ ~ ~ oak_sign{front_text:{messages:['[{"text":" "},{"translate":"gui.cancel"}]','{"text":""}','{"text":""}','{"text":""}']}} replace

(In this example I added an empty space before the translation component)

Right, now I can confirm it.