I don't see why I would need an entire webapp to divide a price tag by my hourly wage.

True enough, I wouldn't require an entire webapp if it only involved dividing a price by my hourly rate.

As x-complexity pointed out, the true value arises when I'm not acting rationally. I won't open a calculator in the heat of the moment, but I will open something that’s designed to interrupt me, slap me with the true cost, start a 24-hr timer, and then redirect the money somewhere meaningful if I choose to skip.

It’s less about the calculation, and more about the friction + psychology + follow through. I basically built the app to be the version of me who shows up when the rational version has left the chat

You're rationally thinking about this, not the impulsive state someone will be in when impulse buying (where math rarely occurs, if ever).

Visually showing alternatives to the impulse buyer adds friction between the user & the purchase, and when compared to the original seamless shopping experience, that's enough to slow down impulse purchases.