You can't give a soul to a brand that never had it.
They had +20 years in the business and have continually failed to build a coherent brand identity out of it.
Nintendo is about fun and focus on family, Sony is about high-end graphics, strong 3P relations and 1P that focuses on storytelling (even their GAAS games, whether hit or flop, has some form of storytelling happening).
What exactly is Xbox except for Gears, Forza and Halo? You could hire an elite team of marketing experts and they'd not be able to crack it.
This is kind of true.
Nintendo doesn't need any explanation, but Sony also built a legacy after 20 years, you can see it when you play Astro Bot and all those familliar things and IP pop up on your screen. It has Playstation written over it and gamers get nostalgic over it. Right now they show the dashboards of all past systems on PS5, and they have retro themed consoles and accessories up for sale.
If you look at Xbox, which has nearly 25 years on the market now, there isn't much to go back to. They had Halo. But they're running this franchise into the ground for about a decade or longer. Gears is another shooter and Forza is a racing game (which in itself is obviously influenced by GT).
They cut ties with Team Ninja that gave them Ninja Gaiden. They tried other IP (like Rare's portfolio) and they were kind of big with FROM back in the day (Otogi, Murakumo, Chromehounds), but they either stopped or let them off the hook. Or refused to acquire studios that delivered good second party output. There isn't much that identifies Xbox. They used to be about Xbox Live and the best place for shooters. Which are in abundance on Playstation for the better part of its existence now too, and since PS4 even were more popular there.