One should not confuse authorisation to enter Switzerland with a request to have a stay authorised administratively.
The first concerns visas and is regulated by the Schengen Agreements which exempt Europeans from this procedure.
The second is the authorisation to stay in Switzerland. For this type of authorisation, a distinction must be made between stays of more or less than 90 days.
During the first 90 days, a European can stay in Switzerland without having to take any action if they are not in engaged in gainful employment or studies (e.g. they are there for tourism, visiting an educational institution/enrolling on site, etc.).
Legal basis: Art 2 para. 4 Annex I AFMP, Art. 9 FMIO
The SEM provides a timeframe calculator on its website.