I've created a MEW wallet and noted the seed (Mnemonic phrase). After playing around with the Brave Browser and its Crypto Wallets plugin, I tried to restore the account from the seed I received from MEW.
My assumption at that point was (I'm still learning) that the Crypto Wallets plugin of Brave is just another Etherum client, and I could use this one in parallel (as long as I restore the keys with my seed).
To my surprise, the recovery worked well, and "an account" was restored and added to the Brave Browser. However, the account has a different public address and, of course, zero balance.
So there must be a misconception in my head.
Why can I restore with my seed but end up with a different account (public address)?
Thanks to this answer, I was able to track down an issue on Brave's Github repository, which explains a couple of incompatibilities with other wallets. IMO this explains the confusing behavior described in my post.