I think you need to enable the teamserver on your project: https://docs.mendix.com/developerportal/deploy/mendix-cloud-deploy
did you create the project in Mendix studio pro or Mendix studio? If you created in the Mendix studio pro, you have to go to the Mendix apps in your developer portal and choose the project that you need to publish in the cloud , and on the left side menu, you can find the team server link open it and there enable it...
Might this helps
A few things I think of;
Please provide a bit more insight in how you started & opened the project. Otherwise answering will be hard.
Did you, in the mean time, link a paid cloud environment to the application?
The sandbox (which is the 'Run’ option) is free, but once you deploy the application on a paid cloud node, the option to run it in the sandbox becomes unavailable.
Is there still a free environment connected?
Follow these steps exactly;
If thats is true; I’m out of clues
If false; you or one of your team members unlinked the app