fix: Replace Desktop util with built-in BrowserUtil (fixes #6020)

[exigow]

Description

I had the exact same issue as in #6020 when setting up the extension locally. Every attempt to log in ended in a freeze (100% reproducible).

My change removes the Desktop class and replaces it with a built-in OS-agnostic BrowserUtil. Removing this class also removes the use of the SLF4J logger, which was the cause of the mentioned exceptions.

Checklist

• ✅ I've read the contributing guide
• ✅ The relevant docs, if any, have been updated or created
• ✅ The relevant tests, if any, have been updated or created

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[exigow]

I have read the CLA Document and I hereby sign the CLA

[Patrick-Erichsen]

Wow, didn't realize we had a hand-rolled browser util implementation when there is a built-in from IntelliJ. This was likely a very old artifact from one of the original OS contributors that helped us set up the original JetBrains plugin.

Great find!