If I place the cursor on input or file and press **ctrl+up** then the cursor jumps to the next instance of the word, but if I place the cursor in the middle of **=>** and press **ctrl+up** nothing happens even though there are other **=>** present in the file.
This doesn't look like a stock Geany configuration; as @codebrainz said <kbd>Ctrl+Up</kbd> just skips a paragraph in the stock configuration, so if it really jumps to the next occurrence of the current word it means you either have a plugin enabled, or changed the <kbd>Ctrl+Up</kbd>/<kbd>Ctrl+Down</kbd> keybindings to something else, maybe *Find Next/Previous Selection*. Those two use either the current selection or the current "word", which as @codebrainz mentioned would have then to be defined differently if you'd like it to include non-wordchars.