When it comes down to colors and symbolisms, Thrawn's been very consistent with his color of choice: both in Legends and Canon, anything burgundy means Thrawn.
In heraldy, the tincture gules (red) symbolizes a warrior or martyr, and denotes military strength and magnanimity. Pretty fitting ๐โโ๏ธ
In both Canon and Legends, burgundy is the Mitth family color and as it is tradition for warriors belonging to a ruling family, Thrawn wears a burgundy patch on his uniform in Outbound Flight and in Alliances:
ยซHis eyes were glowing red, his skin blue, his hair blue-black. He was dressed in a black military-style uniform with a burgundy patch on one shoulder and silver bars on his collar.ยป Timothy Zahn, Thrawn Alliances, 2018
ยซHe wore the same black as their escorts, but with a larger burgundy patch on his shoulder and a pair of elaborately tooled silver bars on his collar.ยป Timothy Zahn, Outbound Flight, 2006
But Thrawn's association with the color actually dates back to 1998 as it is the color of the uniform of Thrawn's Household Phalanx, and later becomes the color denoting members of the Empire of the Hand.
ยซFive meters beyond that, right at the room's back wall, were six more of the blue-skinned aliens, all wearing the same tight-fitting burgundy patchwork-design outfits as the ones who had escorted her here from the slideway.ยป Timothy Zahn, Vision of the Future, 1998
Interesting how the Phalanx's warriors wear a "patchwork-design outfit", just how in Canon Night Troopers' armors are patched together by burgundy strips of fabric. Captain Enoch himself wears burgundy garments and red gloves:
Even before his Peridea exile, Thrawn has used burgundy in the symbol of the Seventh Fleet:
It's interesting to note how Thrawn basically adopted it as his own color despite not being in good terms with his family... not in Canon and especially not in Legends.
It also happens that those associating with him already wear a shade of red of their own. This is particularly evident in Canon, as red is the color that identifies the Nightsisters and it holds a very strong connection with anything Dathomirian. It is wore by the Nightsisters, by Morgan Elsbeth, the Great Mothers and I would add Captain Enoch too.
In Legends, bloodred is the color of Soontir Fel and the 181st Fighter Wing. A red stripe is found on their fighters' wings and on the pilots' uniform a uniform Fel kept wearing during his service in the Empire of the Hand.
Canon Thrawn, just as his Legends counterpart, likes setting himself apart. He heavily customized the Chimaera, his men wear his own personal symbol on their uniform, and since his first years in the Empire, he's been building a very exclusive and unique faction not necessarily linked to the Empire or the Ascendancy by meticulously hand picking his followers.
Even more so after the ten years he spent on Peridea.