I'm planning on deploying my (React) web app in a Microsoft Teams app. While it's clear that you can do that for custom apps used in your domain, I don't find any information about doing this for a third party app that would be available for everyone on the Teams store. Is this the same, apparently quite easy, process ?
Yes, in simple terms, it's basically the same. You can see more in the docs here: https://learn.microsoft.com/en-us/microsoftteams/platform/concepts/deploy-and-publish/appsource/publish . Some differences are:
You might want to test it better, if it's going to such a wide audience you can't control/engage with easily.
Security is probably more important when going to a public audience. For instance, you probably want to enable SSO - https://learn.microsoft.com/en-us/microsoftteams/platform/tabs/how-to/authentication/tab-sso-overview
Your graphics (icons) need to match specific guidelines
Your title, description and more are all vetted to make sure that they match certain guidelines.
All of this is documented in my first link above.