Interesting points! Thanks.
I didn't know "inscrire" is a transitive verb, so indeed "s'inscrire à" is grammatically incorrect.
As often with french it raises the question of "does this rule make sense regarding usage". A quick google search for "s'inscrire à une salle de sport" shows a lot of results, even from people specializing in sport. And many native speakers were fooled by this rule.
As for the "crédit", the dictionnary definition seem to state it is correct (even though "bon" would be a bit better).
https://larousse.fr/dictionnaires/francais/cr%c3%a9dit/20314...
Crédit: Autorisation de dépenses accordée par les autorités qui établissent, votent ou règlent les budgets ; somme ainsi allouée : La bibliothèque dispose d'un crédit de dix mille euros.
Transitivity is not an issue: "obéir à ses instincts" and "suivre ces instincts".
So "s'incrire à" is not incorrect per se, e.g. "s'inscrire à des cours de danse". Even, you must say "s'inscrire à la mairie" (e.g. for poll lists) and not "s'inscrire dans la mairie".
I think that what is technically correct is to use "à" when you talk about where you sign in or register (usually a one-time action) and "dans" when you talk about signing in to perform a recurring activity.
That little à word derives from the Latin words "ab" and "ad", which you can find in words ("adjacent", "adverb", "addition", "adventure"... hemmm I mean *aventure"; sometimes English is more Latin than French) which tell the idea of proximity or direction.
Both "s'inscrire à" and "s'inscrire dans" exist. The trick is to pick the right form. Both may be correct in some cases, but not in others.
Sometimes the meaning changes as well. For example "s'inscrire à l'école" and "s'inscrire dans une école". The latter means "to register with a school" but the former is more "to register to start school" in the sense that it is 'school' in general.
As for "crédits", indeed the meaning is basically the same as in English and the original sentence is correct in the language. But it's not something anyone would say. The terms used would most likely be either "bon" (voucher) or "forfait" (inclusive special rate), or perhaps "chèque" (cheque) instead of "bon" if it was given by your employer as a benefit.
As for the "crédit", the dictionnary definition seem to state it is correct (even though "bon" would be a bit better). https://larousse.fr/dictionnaires/francais/cr%c3%a9dit/20314... Crédit: Autorisation de dépenses accordée par les autorités qui établissent, votent ou règlent les budgets ; somme ainsi allouée : La bibliothèque dispose d'un crédit de dix mille euros.