feat(stepfunctions): Start Execution launching Execution Details (#7741)

## Problem
Currently Start Execution only outputs the execution arn to the output

## Solution
Adding a call to execution detail provider after starting an execution,
launching the execution details webview ( Also works with express
executions )

## Verification

![test8](https://github.com/user-attachments/assets/9c000d28-3563-42d0-aa93-5945ea4ba7c0)


---

- Treat all work as PUBLIC. Private `feature/x` branches will not be
squash-merged at release time.
- Your code changes must meet the guidelines in
[CONTRIBUTING.md](https://github.com/aws/aws-toolkit-vscode/blob/master/CONTRIBUTING.md#guidelines).
- License: I confirm that my contribution is made under the terms of the
Apache 2.0 license.

---------

Co-authored-by: Diler Zaza <[email protected]>

Author: l0minous

packages/core/src/stepFunctions/vue/executeStateMachine/executeStateMachine.ts

@@ -15,6 +15,7 @@ import { ExtContext } from '../../../shared/extensions'
 import { VueWebview } from '../../../webviews/main'
 import * as vscode from 'vscode'
 import { telemetry } from '../../../shared/telemetry/telemetry'
+import { ExecutionDetailProvider } from '../../executionDetails/executionDetailProvider'
 
 interface StateMachine {
     arn: string
@@ -61,9 +62,15 @@ export class ExecuteStateMachineWebview extends VueWebview {
                 stateMachineArn: this.stateMachine.arn,
                 input,
             })
+            await ExecutionDetailProvider.openExecutionDetails(
+                startExecResponse.executionArn!,
+                startExecResponse.startDate!.toString()
+            )
             this.logger.info('started execution for Step Functions State Machine')
             this.channel.appendLine(localize('AWS.stepFunctions.executeStateMachine.info.started', 'Execution started'))
             this.channel.appendLine(startExecResponse.executionArn || '')
+
+            this.dispose()
         } catch (e) {
             executeResult = 'Failed'
             const error = e as Error

packages/toolkit/.changes/next-release/Feature-eb3fdb2e-b75b-4789-8b2f-e18130aa1ccf.json

@@ -0,0 +1,4 @@
+{
+	"type": "Feature",
+	"description": "[Step Functions] Start Execution option in the AWS Explorer now opens the execution details page after clicking Execute"
+}