This expression doesn't only mean stop, it can also mean slow down (just like you can use brakes in a car to stop or to slow down).

You provided a link to a dictionary that only mentions slowing down – and I've upvoted your question for showing your research. However, it's often good to check more than one dictionary, as sometimes a dictionary won't quite capture all the possible usages of a word.

In this case, we can find more at Cambridge, which says:

put the brakes on to slow down or stop an activity : The city has put the brakes on further spending.

or at Collins, which says:

brake (noun) You can use brake in a number of expressions to indicate that something has slowed down or stopped : Illness had put a brake on his progress.

The expressions hit the breaks and put the brakes on are pretty much interchangeable when it comes to these metaphorical usages.

This expression doesn't only mean stop, it can also mean slow down (just like you can use brakes in a car to stop or to slow down).

You provided a link to a dictionary that only mentions stopping – and I've upvoted your question for showing your research. However, it's often good to check more than one dictionary, as sometimes a dictionary won't quite capture all the possible usages of a word.

In this case, we can find more at Cambridge, which says:

put the brakes on to slow down or stop an activity : The city has put the brakes on further spending.

or at Collins, which says:

brake (noun) You can use brake in a number of expressions to indicate that something has slowed down or stopped : Illness had put a brake on his progress.

The expressions hit the breaks and put the brakes on are pretty much interchangeable when it comes to these metaphorical usages.