Short answer: Cartier — specifically a diamond-set Cartier Santos Demoiselle — is the luxury watch most directly linked to Taylor Swift’s engagement announcement. (businessinsider.com)

Other luxury watch/horology brands that media outlets have connected to Swift around the engagement era (either because she’s worn them recently or they’ve been part of related coverage):

• Louis Vuitton (Tambour) — spotted on Swift at Chiefs games and other appearances. (people.com)
• Rolex (Day‑Date 36) — reported in coverage of high‑value gifts Travis Kelce reportedly gave Swift. (instyle.com)
• Concord — a vintage Concord watch was famously worn by Swift as a choker at the 2024 Grammys (often cited in writeups of her watch choices). (gq-magazine.co.uk)

If you want, I can pull up the exact photos/articles that identify the Cartier Santos Demoiselle in the engagement pictures.