One of the institutions in Switzerland that is competent to recognize many types of foreign qualifications is the State Secretariat for Education (SERI). However, there are others. Refugees from Ukraine can find important information on how to get their qualifications recognized, in German, Ukrainian and Russian, on the SERI website.
The site also has information specifically about applications from people with an S permit.
You can apply to the SRK to have healthcare qualifications recognized (https://www.redcross.ch/de/unser-angebot/gesundheitsberufe-anerkennung-und-registrierung/anerkennung-auslaendischer-diplome "Recognition of foreign qualifications in the healthcare professions").