Simplified path. The puzzle showed the main steps; the full route is being checked.
Greek
kamara
‘A vault’
into Latin
Latin
camera
‘An arched roof’
into Middle English
Middle English
chambre
‘A room’
became English
English
chamber
‘A room or enclosed space’
The story of chamber
Chamber begins with Greek kamara, a vault, and Latin camera, an arched roof. Through later Latin and French the word came to name a room. English chamber carries both a change in sound and an expansion from a covering to an enclosed space.
These are selected stages, not every spelling or intermediary. The story identifies omitted links; older forms did not all disappear at once.