Sync eng/common directory with azure-sdk-tools for PR 14709

[azure-sdk]

Sync eng/common directory with azure-sdk-tools for PR Azure/azure-sdk-tools#14709 See eng/common workflow

[Copilot]

Pull request overview

Syncs the eng/common MCP installer script with upstream azure-sdk-tools changes related to azure-sdk-tools PR 14709, focusing on how the azsdk CLI MCP server is installed and launched.

Changes:

• Hard-codes the azsdk CLI package identifiers in the installer script (removing -FileName / -Package parameters).
• Adds an “already installed + up-to-date” fast-path using azsdk upgrade --check --output json.
• Updates the run invocation to use the mcp subcommand and propagates the child process exit code.

Comments suppressed due to low confidence (1)

eng/common/mcp/azure-sdk-mcp.ps1:156

• In the non--Run path, the Install-Standalone-Tool call ends with a line-continuation backtick after -Repository $Repository, but there’s no subsequent continuation content. This leaves the script syntactically invalid (it will fail to parse before executing). Remove the trailing backtick (or add the missing continuation) so the installer path can run.

        -Package $packageName `
        -Directory $tempInstallDirectory `
        -Repository $Repository `

}