What is the ruling on drinking a commodity (such as water) from a commercial store before paying for it, and is this considered a sale in which possession has not been taken, rendering it invalid? And what are the Sharia rulings that stem from that?

If the store prohibits taking the bottle before payment, then it is not permissible to take it until its price has been paid, due to the Almighty's saying: {And do not consume your properties among yourselves through falsehood, except for a trade by mutual consent from among you}, and due to the Prophet's (peace be upon him) saying: "Indeed, selling is by mutual consent."

One must seek forgiveness and pay the price of the bottle.

However, if the store does not object to taking it before paying the price, then there is no harm.