MetaMask extension overrides the Brave wallet provider

[FounderCasey]

Description

In #21949, it's mentioned that isBraveWallet is added; however, if the MetaMask extension is installed, Brave's isBraveWallet isn't found anymore. MetaMask likely overrides it as a provider.

Steps to Reproduce

1. Have more than two wallet extensions(Coinbase Wallet and MetaMask, for example)
2. We're able to detect three providers with ethereum.providers
3. Disable the Coinbase Wallet extension, leaving just the MetaMask extension active
4. We're no longer able to detect Brave's provider

Actual result:

• When the MetaMask extension is disabled, and Coinbase Wallet is enabled, we get the proper result. Both isCoinbaseWallet and isBraveWallet exist
  

• When the MetaMask extension is enabled, and CoinbaseWallet is disabled, we no longer get the Brave provider

• When both MetaMask and Coinbase Wallet are enabled, we get all three providers
  

Expected result:

The Brave provider is always there.

Reproduces how often:

Easily reproduced

Brave version (brave://version info)

1.41.96 Chromium: 103.0.5060.114 (Official Build) (64-bit)

Version/Channel Information:

• Can you reproduce this issue with the current release?
  • Yes
• Can you reproduce this issue with the beta channel? NA
• Can you reproduce this issue with the nightly channel? NA

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields? No
• Does the issue resolve itself when disabling Brave Rewards? No
• Is the issue reproducible on the latest version of Chrome? N/A

Miscellaneous Information:

[luisgj]

Coinbase wallet prepares the providers array to address the compatibility issue. Right now to use brave wallet and co exist with metamask you must set your Default Crypto Wallet setting to Brave Wallet (not Prefer Extensions) to prevent the override and Brave Wallet (Prefer Extensions) when you want metamask to override brave. :(

[ccali11]

Does Brave have an API where we can control the default wallet setting programmatically?