You can refer the following URL for sold out badge
You have to check your theme setting to enable your sold out badge and you can change colors as well.
Eunice here from the Shopify team, welcome to the community! That's a great question, I'd be happy to solve this issue with you.
To add a sold-out notification on specific products you need to ensure you're tracking the inventory for the products that have sold out. To do this just head to your chosen product from your Shopify admin and scroll down to the Inventory section:
When 'Track quantity' is left un-ticked customers will still be able to checkout with products that have sold out.
If this is the case with your store, I advise sending an email to the customers who've purchased an out-of-stock item. Kindly inform them that there may be a delay in shipment.
Thanks for providing your store URL by the way. It's looking good! I really like the fresh and natural colors; it totally aligns with your target audience! The one thing I did notice is that while you have a decent following on Facebook and Instagram, there's not much engagement. To improve this and level up your social media presence I recommend taking this free course by Gretta van Riel, one of Australia’s top young serial entrepreneurs. Gretta shares her tried and tested tips and tricks to grow your following, engagement, and business on Instagram.
Hope this all helps, if you have any questions don't hesitate to sing out here.