[dotnet-watch] Review browser launching/refresh corner cases

[tmat]

We don't have many tests covering browser refresh and browser launching.
We should increase test coverage and handle following cases:

• BrowserRefreshServer may be created even when no browser is launched.
• When a project is restarted it may change the launch URL. We should not reuse BrowserRefreshServer in such case.

Note: Issue #9038 tracks moving browser launching to dotnet run.

[dotnet-issue-labeler]

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[dotnet-issue-labeler]

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