2027 Social Security COLA looks like ~3.5% — does that actually change when I should claim?

Projections (Senior Citizens League and others) have the 2027 COLA around 3.4-3.6%, with the official number announced Oct 14 — likely the biggest bump since 2023. I'm 59 and weighing claiming at 62 vs 67. Question: does a big COLA year actually change the break-even math, or is the claiming decision the same ~8%-a-year story regardless? Every article covers the headline number and nobody explains whether it moves the decision.