Advice on encroaching lawn variety

With photos! 🤦🏼‍♀️ I have Buffalo Lawn, but this different, smaller leaf, almost teal coloured variant has taken off and seems to be taking quicker than the Buffalo. The lawn area itself is quite patchy, my main goal is to fill in the dirt patches so I’m not trecking dirt and mud around, but is letting this grass grow in going to be of detriment come next spring?

📍Australia, ~30°C at the moment