Where is my wallet's master key stored?
You think your wallet stores your master key somewhere, but it doesn't: it's calculated every time you restore your seed.
**Your master key is not stored anywhere: it is calculated.**
Nobody stores it: it's calculated
Your wallet does not keep your master key in a file or on a server. It does not look it up anywhere when it needs it.
The BIP-32 standard defines how it's obtained. The source says verbatim: Calculate I = HMAC-SHA512(Key = "Bitcoin seed", Data = S). That function produces your master key from your seed.
That's why the same backup works in any wallet
The calculation is deterministic: if you restore your seed in another piece of software that follows the standard, you get exactly the same master key. Brand and operating system don't matter.
No wallet can 'look up' your master key elsewhere, because it isn't stored: it derives it every time from your seed.
What this means for your backup
You don't need to export the master key or keep it separately. Your backup is the seed, and that's enough to rebuild everything.
Anyone who has your seed can calculate the master key. That's why the paper where you wrote it down is the most important thing.
This doesn't prove your seed is the master key
Just because the master key is calculated doesn't make it public: without your seed, nobody can get it. And it's not the same as your seed: they are two different pieces of the same process.
Source: BIP-32, generacion de la clave maestra