There will be additional codes.
To be fair, content focus is decided by Patreon polls, not me. Every character gets some content each update, but the winner of the poll gets bigger focus. I do balance it a little by not allowing the winner of the poll to be an option in the next poll, but if people choose the same character every other poll, then their story will pull ahead. So far, Amy has won every poll she has been an option for so has more content than other characters.
That is also the reason why outside of Serena and Amy, no other characters storylines are currently linked. You can progress each character at whatever rate you want. So yes, currently you may be waiting for specific days for Katie, you can skip through to the days you want without penalty to other stories. Subsequently, if you want to ignore Katie and focus on another character (all of which have the chance to progress their story every day) you can do that too.
As it is, it doesn't really matter what speed people progress the characters at. And I said before, Katie is getting more events, some of which can be done early game and additional options in those events will open later as you progress her story. One of which will be in the next update. Unfortunately that's just the way development is. I'd love to have Katie have actions to be done every day, but that would mean focusing entirely on her and ignoring everyone else for an update or two as there are a lot of possible interactions to be added for her.
As you said, it's only 0.4, so hopefully you'll feel like things are less sluggish in a couple of versions.