Are the laws prohibiting handling muktzeh on Shabbat considered biblical (from the Torah) or rabbinic? The reason it matters is because of the rule in Halacha, Safek Derabbanan Lekula vs Safek d’oraita lechumrah.
Sources for this please.
Mukktzeh is d'rabbanan.
R Daniel Braude writes (Learn Shabbos, p. 442)
There is a Rabbinic prohibition to handle items that are muktzeh on Shabbat
He spells out some of the reasons the Sages enacted these laws, e.g., to ensure Shabbat remains a day of rest and that we don't use "weekday objects" (Rambam), to prevent people from carrying these items in forbidden areas (Raavad), to prevent us from doing forbidden work with items that likely would lead to do so.
R Eliezer Melamed writes similarly
The Sages prohibited moving things that are not fitting for Shabbat and that one puts out of his mind