All un-paid Pico-8 games on st33d.itch.io are released as Creative Commons works. They can be copied, hosted, and remixed by anyone with proper attribution.
"If your project isn’t a mobile game, that’s totally fine!"
This line betrays a lack of awareness of what a "Pico-8 game" is. Pico-8 is an 8-bit fantasy console that executes a single bespoke file of limited size. It can export binaries for all the targets you can already see on this page (including HTML, with on-screen mobile controls). This is the problem you will be solving.
Should you build a Pico-8 solution in your app, you are welcome put Metrash, Pak Pok, Flip Knight, or other un-paid Pico-8 games of mine in it. I am sure there are other Pico-8 creators who would be equally generous should you approach them with this solution in place.
Sadly, I will not be creating an account on your app. No disrespect, but I used to make Flash games for a living and I am sick of filling out forms for yet another hosting portal. I sympathise that this may create unwanted busywork for you, but I hope you will take comfort in my enjoyment of doing none of it.