To switch a payment provider from 'test' to 'live' mode, go to Payment providers and select the desired payment provider.
In order to use Payrexx productively, the mode must be set to "Live". If you select "Test", you can try and test everything in a test environment. This activation does not take place automatically and must be adjusted manually!
Note: If you can't select the Test mode at Payrexx by Stripe, try to deactivate and then reactivate Payrexx by Stripe. That should fix the problem.
If you cannot deactivate Payrexx by Stripe, please check if you have any other active payment service provider. If not, you should activate another PSP (because there needs to be at least one active PSP). You can e.g. activate "invoice", then deactivate and re-activate Payrexx by Stripe and remove "invoice" after that.