Where are you reading 1 cent/month? The cheapest way I can see to run a small app+db project on Heroku now is to use an Eco dyno at $5/month with a Mini Postgres instance at $5/month, for a total of $10/month.
If you don't want your project to sleep, you probably want a Basic dyno ($7/month) instead of an Eco dyno.
As of now, https://elements.heroku.com/addons/heroku-postgresql says $0.01/month and their CLI as of Wednesday also said that. Of course, this feels like a weird workaround until December 1 since they also say that's when they're going to saying charging for it.
Just found this too. The brand-new Eco plan costs $5/mo, shared over all projects up to 1000 dyno hours, and then it seems each database on the Micro plan is $0.01 per month. That comes out to $5.05 per month for me I believe for my 5 portfolio projects? Maybe there's hope for Heroku yet.
If you don't want your project to sleep, you probably want a Basic dyno ($7/month) instead of an Eco dyno.
Am I missing something?
Edit: I meant to add a link to the pricing page.
https://www.heroku.com/pricing