The technology at the moment would either be LiPo or good old Lithium Ion, the real issue is finding a manufacturer that has a cell with a high enough capacity in the form factor you need, the selections are very limited, and most of the people who just started doing smart watches are investing in that tech for themselves since it’s still a very niche market.
It also usually comes down to very aggressive packaging design, every fraction of a mm counts, so getting a battery with the minimal amount of casing and structure is key.
If this is for a production project, you’d have to talk to your battery suppliers and see if they offer anything in that compact of a package, and ask for a road map to understand if and when they might be introducing those products in the future. If it’s for a student/concept project, then just say it’s LiPo and call it a day.