Prevent kids from "accidentally" making purchases in Steam

You can use Family View to restrict what your kids can do with your Steam account, including preventing them from accessing the store. This works by setting a 4-digit PIN that is used to log in as an adult within your account.

You can enable this and configure what parts of your Steam account are off-limits by going to Settings → Family and clicking on Manage Family View.

You'll want to leave the Steam store checkbox unchecked.

You can't buy things from steam without billing information. So, I would suggest to:

1. Clear billing information in child's account and stop using it for purchases. (On the top right of the steam window, click the child's username, and choose Account Details. Under Store and Purchase History, find the saved payment method(s) and hit Delete)
2. Setup your own steam account.
3. Buy games using your own account (buy as a gift) and gift them to your kid.

This will prevent game purchases AND "in-game" purchases.

Another potential option, if none of the above work, is to put the steam client into "Offline" mode. Then they can get online and play those games that are actively downloaded/installed but they can't play uninstalled games, or go to the store and buy any additional games. Family options might be a better idea though.