We are allowed to dye the grey/white beard / head hairs except with black as this is deceiving making you look younger than you are. However if your natural hair colour is not black but brown, then isn't dyeing your hair with brown also deceiving? Rather in this case, black would be more appropriate? See https://islamqa.info/en/476
The underlying reason dying one's hair black is forbidden is because of ahadith:
"Some people will dye their hair black like the breasts of pigeons at the end of time, but they will not even smell the fragrance of Paradise."
Sunan an-Nasa'i 5075 [grade: sahih]
Jabir b. 'Abdullah reported that Abu Qubafa was led (to the andience of the Holy Prophet) on the day of the Conquest of Mecca and his head and beard were white like hyssop, whereupon Allah's Messenger said: Change it with something but avoid black.
Sahih Muslim 2102 b (see also Sunan an-Nasa'i 5076 [grade: sahih])
Some (but not all) scholars are of the opinion this is because it is a form of deceit:
... the reason mentioned – namely cheating and deception – is an implicit reason which some of the scholars stated was what was meant here ...
Islam Q&A, 2010
But there's other opinions:
In this case, it seems reasonable to suspect that deception is not the (sole) underlying reason.
Indeed, ahadith such as Sahih Muslim 2341 a and Sunan an-Nasa'i 5071 [grade: sahih] indicate it's fine to dye one's hair (see also Why has black hair dye been singled out?), and there's no logical reason to believe that dyed-black hair disguises an individual's age any more than dyed-brown hair (particular for dark shades). In fact, for women observing hijab, it seems even more illogical.
It's possible there's more to this than we're aware of. E.g., it might be deceptive for a proportion of the ummah (as a whole) to dye their hair black. Or perhaps there would be a few people who use it for deception, but the rules need to apply to everyone.
In any case, the ahadith remain, whether or not we understand the reason behind them.