Migrate from proposed API `terminalDataWriteEvent` to new `terminalShellIntegration`

[Colengms]

My understanding is that the terminalDataWriteEvent proposed API we're using will never be published to stable and has been superseded by another feature.

The code for terminalDataWriteEvent refers to:

// https://github.com/microsoft/vscode/issues/78502
//
// This API is still proposed but we don't intent on promoting it to stable due to problems
// around performance. See #145234 for a more likely API to get stabilized.

#145234 has since been closed as completed, moving terminalShellIntegration out of proposed and into stable.