Hi there, 

In our documentation you'll find a link to create or manage your app. Until you have created an application, the settings dashboard won't appear in your account. While you do need a separate account(s) for any additional app(s) you create, a subscription is not a requirement for creating an API application. 

Am I understanding correctly that if I want to have two versions of one app (development and production), then I have to register another Strava account? With this second account, I can register the second version of the app.

I have a development and production version, both using the same client. The redirect_uri passed to Strava during oauth authentication changes, and that's how I distinguish between the two. Once you have the auth token there's no difference in how you use it, so being on production vs development makes no difference. The only other special case is with webhooks. For that I use a flag in my database to indicate if a user is on production vs development. When the webhook comes in, I redirect it to either the production or development webhook handler depending on the value of that flag.

Using a second account with a separate client and keys is also entirely reasonable and may be easier depending on how your app is set up. It really comes down to how you want to manage things and what works best in your situation.

FWIW I have 3 apps (a personal one for https://run.dblock.org/, https://slava.playplay.io/ and https://strada.playplay.io/) and I do find this annoying as well. Every sane platform I know lets you create and manage apps without creating multiple accounts. I create multiple with email+appname@... and just live with it.