Don’t worry about the singing not working yet.
Trying to combine playing and singing is hard enough, especially if you still need to engrain that muscle memory of timely chord changes. As long you can’t do that ‘quasi in your sleep’, singing will feel like an ordeal that will make your strumming engine sputter.
There is no shame putting singing on standby for a while and revisit when you are able to feel the rhythm while strumming, so you can have your playing going on autopilot.
About that auto-pilot: