Your not giving the full definitions of your “other examples”.
in regards to “age” it means time occupied by a generation
(an age (i. e. the time ordinarily occupied by each successive generation), the space of from 30 to 33 years)- thayers.
In regards to “men of same stock”. It means:
1.) those of a successive genealogy as in “14 generations from Abraham to David”.
2.) race of men with similar characteristics, such as the “wicked generation that asked Jesus for a sign.”
Now let’s look at where thayers puts the definition of genea in Matthew 23:36 and Matthew 24:34:
the whole multitude of men living at the same time:
Matthew 24:34;
Mark 13:30;
Luke 1:48 (πᾶσαι αἱ γενεαί); ;
Philippians 2:15; used especially of the Jewish race living at one and the same period:
Matthew 11:16;
Matthew 12:39, 41f, 45;
Matthew 16:4;
Matthew 23:36;
Mark 8:12, 38;
Luke 11:29f, 32, 50;
Luke 17:25;
Acts 13:36;
Hebrews 3:10; ἄνθρωποι τῆς γενεάς ταύτης,
Luke 7:31; ἄνδρες τῆς γενεάς ταύτης,
Luke 11:31; τήνδέ γενεάν αὐτοῦ τίς διηγήσεται, who can describe the wickedness of the present generation,
Acts 8:33 (from
Isaiah 53:8the Sept.) (but cf. Meyer, at the passage). Thayers
All the definitions include those living at the same time. The only definitions of genea that include through time or history is when genea is plural as in “14 generations from Abraham to David”, or written as “generation to generation”.
I honestly have no idea where you are getting your definitions from or if you are just misunderstanding the definitions provided?