There is generally a large Easter market in Siena but not any particular event other than masses - https://www.discovertuscany.com/tuscany-events/easter-in-tuscany.html
Most restaurants will be open on both days, while grocery stores do close for both days. If you're in an apartment, make sure you buy food ahead of time to have for those days, particularly if you don't want to be out and about on Easter -- restaurants do get crowded and booking ahead is recommended.