I'm sorry to hear you're having trouble with setting your availability in the Shopify Ping app. You should be able to reach the chat availability feature by clicking on the Settings icon from the top right-hand corner of Shopify Ping's home screen, then clicking on "Chat availability" under the 'Store' heading. (See below.)
From the chat availability screen, you can then choose whether you want to be available at all times, or if you would like to break your availability down by specific days. (See below.)
If this is not what you're seeing, then please provide a screenshot of what you're seeing on your end. You'll also want to ensure your device is updated to the latest iOS version.