Will there be no more updates for house chores? 

no they are working on the summer update i think coming this month since the game is barely not done yet if you read the 0.17 update description theres is more updates to come

also i saw their patreon and the 0.18 update might. Come out half of may or late may or so and house chores is a work in progress meaning more updates are coming 

they make posts on patreon, you don't have to pay to see their activity, so check there