[Feature Request]: Allow launching Profiler with existing sessions without requiring a new Session Name

### Feature Description

Provide the option to launch the Profiler using previously created sessions or default templates, rather than forcing the creation of a new session name every time. If a user cancels or closes the "Session Name" prompt, the Profiler should still open (or prompt for a session selection) rather than aborting the launch entirely.

### Problem and Motivation

In Azure Data Studio, when you start the Profiler, the "Session Name" prompt is optional. If you cancel it, you can still access the Profiler interface and select an existing, previously created session or standard template.

Currently, in the VS Code MSSQL extension, the "Session Name" input is treated as a hard requirement. If a user cancels this prompt, the Profiler completely fails to launch. This hurts the workflow for developers who reuse standard tracing/profiling templates and don't want to clutter their SQL Server with a brand-new session name every single time they want to view a trace. Bringing this behavior in line with Azure Data Studio would greatly improve parity and user experience.

### Related Area

- [ ] Connection dialog (SQL Server | Azure browse/Fabric browse)
- [x] Query editor
- [x] Query results panel
- [ ] Object Explorer
- [ ] GitHub Copilot integration
- [ ] Preview/Edit data
- [ ] Table Designer
- [ ] Schema Designer
- [ ] Schema Compare
- [ ] Local SQL Server Container provisioning
- [ ] SQL database in Fabric provisioning
- [ ] DACPAC/BACPAC export/import
- [ ] SQL Database projects
- [ ] Query Plan Visualizer
- [x] Other (please describe below)

### If you selected "Other", please describe the area

Query Profiler

### Confirmation

- [x] I have searched existing feature requests and couldn't find a match
- [ ] I want to help implement this feature

Start by locating the Query Profiler launch flow and the Session Name prompt in the TypeScript extension. Compare the current cancellation behavior with the Azure Data Studio workflow described here; done means the Profiler opens after cancellation and lets users select an existing session or default template.

Written by the indexing model from the issue text.