With 16 con and 15 str, you will still be a great barbarian.
To get those rolls you are assuming rolling well above average or getting bonuses to Constitution on point buy (which it is unlikely a Sage will IMO).
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That extra wisdom might help you perceive something or resist a mind control effect once in a while. Your spells/rituals will make your utility greater as that of a regular barbarian. So no, you are not actively hindered in playing your barbarian by just taking the sage background.
Except on point buy your Wisdom will be lower than if you had the same Strength and Constitution and got the bonus in Strength or Constitution.
This is the fallacy here - the bonus on Wisdom does not mean a higher Wisdom. On point buy, with a 15 Strength and 16 Constitution after a bonus to Con and Wisdom you will actually have a lower Wisdom than you would have with a 15 strength and 16 Con after a bonus on Strength and Constitution.
So you won't be able to percieve or resist better or resist mind effects better you will actually be worse at that than if you got the bonus on Strength instead. The only way you are better at Wisdom is if you dump strength, dexterity or constitution below 14.
Here are two point buy Barbarian builds with 15 Strength and 16 Con, both of these are legal in point buy with the bonuses applied where noted. They have the exact same Strength, Dexterity, Constitution and Charisma scores. The character with a +2 in Wisdom has a
LOWER Wisdom on point buy (and a lower intelligence)
Wisdom +2 and Con +1: S15, D14, C16 (15+1),
W12 (10+2), I8, CH 8
Strength +2 and Con +1: S15 (13+2), D14, C16 (15+1),
W13, I9, CH8
With Strength, Dexterity and Constitution the same your Wisdom score is LOWER on a point buy Barbarian if you put the +2 in Wisdom instead of Strength .... your intelligence is lower in this example too if you put the bonus on Wisdom (although that is a choice between Intelligence and Charisma)