[release/6.0-staging][wasm][debugger] Remove error message when browser is closed #85062
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Description
Only skipping printing the error if we have an exception of type: WebSocketException
Customer Impact
https://devdiv.visualstudio.com/DevDiv/_workitems/edit/1784268

When the browser is closed an exception is printed to console.
Regression
Yes, when we backported the communication from .net7 to .net6 to fix other issue, we regressed this and started printing the disconnection exception again.
Testing
Manually tested
Risk
Low risk. Only not printing the error.
Package authoring signed off?
N/A
IMPORTANT: If this change touches code that ships in a NuGet package, please make certain that you have added any necessary package authoring and gotten it explicitly reviewed.