You were not hurt, received a shock, nor in danger. I have had bulbs, chairs, glass table tops break over my 20plus years in hotels. I would not expect compo for flawed item breaking (or maybe mistreated by prev guests item breaking), and in same vein not expect to be charged to replace such items.

Just report to frontdesk asking for a replacement. No need to worry about a repeat or changing hotel. I'd put it down to lamp being abused by a prev guest.

No compo due, you should not even be considering you should get something. Based on your location (SFO) I'd say you are jumping on the current USA compo entitlement culture at slightest chance.