If we could understand it, we wouldn't be us.

90% of the time, dónal finn is in browns while hero fiennes tiffin is in blues/cool greys (in fact, blues and greys become sort of...holmes family coded, by the time we get to the latter episodes, but I will get to that in a moment)

most obvious example is here:

this changes when they're in paris and they go into disguise (Sherlock in brown which is meant to visual signify he is NOT SUPPOSED TO BE SHERLOCK because he's NOT IN BLUE) and then again twice in constantinople when they almost all swap to what I universally call the Desert Khakis™

this is partially practical (light colours reflect light more than dark colours, making them generally cooler to wear) but is also functional as most of the bg extras are dressed in dark tones, allowing the leads to stand out in crowd scenes.

but even in this palette swap, colour-wise they are telegraphing a few things--remember what I said re: Holmes = Blue? when they are introduced to fake Beatrice, they try to use that visual language to signal that association:

Note all the blue accents in Mycroft, Cordelia, and Fake Beatrice's outfits.

Note that even Young Beatrice follows this rule.

I have a couple of theories re: the introduction of yellow and the colour palette swap for Sherlock--both ultimately lead back to Silas Holmes.

Let's start with Sherlock:

I think the show introduces brownish red in Sherlock to tie him to Silas. Silas is determined to emphasize Sherlock as his son and heir and their clothing reflects this:

Note how Sherlock's tie matches both Silas' robe AND Beatrice's shirt and the striping in her skirt--tied by blood and the ambition of their father.

Subconsciously, we begin to see them as a set--whether Sherlock wants to be tied to them or not (and you know he DOES)

Moriarty's wardrobe swap is more nebulous but I have a few theories.

Warming up Moriarty's palette and putting him in that chalk stripe inadvertently mirrors the warmth and twill tone-on-tone stripe that Silas has. It's a poor imitation, but an imitation nonetheless. I think there is some plot indication to the ways in which James begins to admire Silas' ambition and goals and mirrors them in himself.

Moriarty's wardrobe is ALWAYS more extravagant than Sherlock's (I immediately think of the brocaded waistcoat he wears in the first episode when they crash that party)--so it's totally par for the course that he would veer to the most saturated version of the Desert Khaki™.

Note that Moriarty's tie is blue! He's trying so hard to be Holmes adjacent in his actions and ALSO in his wardrobe!

BUT WAIT THERE'S MORE!

Unless you are either Italian or me, a person obsessed with mysteries, you may not know that the term for crime fiction and mystery in Italian is giallo which literally translates to 'yellow.' This originates from the usage of the colour in mystery novel covers in Italy during the 20s and 30s. The term is now tied to like...suspense thriller type mysteries now...particularly those with a sinister sort of air about them.

Where else do we see yellow in the show?

The mystery of Beatrice--both sweet child and also hidden accomplice to Silas Holmes.

Hodge--pompous professor secretly funding the research for a mass murder weapon

Shou'an/Xiao Wei -- moments before she drugs Sherlock and we begin to realize she is not who we think she is

James "You know me" Moriarty - future Napoleon of crime

I think costume designer Jany Demime uses yellow for Moriarty at the end to visually signal what we the audience already knows: That we don't know everything about Moriarty that the show presents to us and that neither does Sherlock.