[QA] Metamask icon instead of Bitget icon is shown when connecting Bitget (Ethereum) wallet for the first time

[tsadovska]

Describe the current behavior in detail

Checked on https://wormhole-connect-mainnet.netlify.app/ [Mainnet] with macOS and Google Chrome

1. Enable Bitget extension
2. Refresh wormhole-connect page
3. Select Avalanche network as source chain
4. Click "Connect wallet" button and select Metamask option
5. Select "Bitkeep" option in OKX Wallet notification
6. Check icon next to the wallet icon

Actual result:

• Metamask wallet icon is shown.
• Correct icon (Bitget icon) is shown only after user refreshes the page.
• Bitget option is displayed and Metamask option is no longer displayed after "Bitkeep" option was selected in OKX Wallet notification.

https://github.com/wormhole-foundation/wormhole-connect/assets/10746654/82e7ab6a-5c71-40bf-af1e-a59d3eb24dcf

What is the expected/desired behavior

Correct icon is displayed next to the wallet account.

[tsadovska]

Issue is reproducible on wormhole-connect-mainnet (Connect v2). MetaMask icon persists for the Bitget wallet even after the wallet is re-connected or the page is refreshed.