60岁 = 60 years old
多 = more than --> over --> plus some
60多岁 = over 60 years old = 60-some years old
Similarly:
60人 = 60 people
60多人 = over 60 people -> 60-some people
It has nothing to do with 年代 (era)
60年代 = the 60s era
Similarly:
20年代 = the (19)20s (most would say 上世紀20年代 = the 20s in the last century)
2020年代 = the 2020s era (some might say 本世紀20年代 = the 20s in this century)
Since it is only 2024, you don't have to mention 'the last century' when referring to the 30s era and later
在中国,60多岁已经是退休的年纪了
In China, sixty-some years old is already a retirement age
Isn't it true for most countries? Canada's official retirement age is 65. Some countries may be younger, I presume 70 years old retirement age is quite rare