fix: reject session reuse when existing connection is still active

[ihmily]

Description

When running a Flet app in web browser mode, opening the same URL in multiple browser tabs
causes cross-tab session contamination. Events triggered in Tab1 affect Tab2's UI, while
Tab1 becomes unresponsive.

Root cause: The REGISTER_CLIENT handler in flet_app.py unconditionally reuses an
existing session when the client provides a matching session_id, without checking whether
that session is still actively connected. When a second browser tab inherits the same
_flet_session_id via sessionStorage cloning (standard HTML5 behavior for duplicated tabs),
it steals the session's output connection from the original tab via attach_connection().

Fix: Before reusing a session, check if its connection is still alive
(session.connection is not None). If so, the request is from a different tab — create a
new session instead. This preserves legitimate reconnect scenarios (page refresh / network
blip) where connection is already None after disconnect().

Fixes #6512

Test Code

import flet as ft

def main(page: ft.Page):
    page.title = "Flet counter example"
    page.vertical_alignment = ft.MainAxisAlignment.CENTER

    input = ft.TextField(value="0", text_align=ft.TextAlign.RIGHT, width=100)

    def minus_click(e):
        input.value = str(int(input.value) - 1)

    def plus_click(e):
        input.value = str(int(input.value) + 1)

    page.add(
        ft.Row(
            alignment=ft.MainAxisAlignment.CENTER,
            controls=[
                ft.IconButton(ft.Icons.REMOVE, on_click=minus_click),
                input,
                ft.IconButton(ft.Icons.ADD, on_click=plus_click),
            ],
        )
    )


ft.run(
    main=main,
    view=ft.AppView.WEB_BROWSER,
    web_renderer=ft.WebRenderer.CANVAS_KIT,
    port=6006
)

Type of change

Bug fix (non-breaking change which fixes an issue)

Checklist

• I signed the CLA.
• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• If this PR targets a release/* branch, I added a new record to the active root CHANGELOG.md section
• I have commented my code, particularly in hard-to-understand areas
• My changes generate no new warnings
• New and existing tests pass locally with my changes
• I have made corresponding changes to the [documentation](https://github.com/flet-dev/website) (if applicable)

Screenshots

Additional details

• Only 1 file changed: sdk/python/packages/flet-web/src/flet_web/fastapi/flet_app.py
• The fix is backward-compatible: legitimate single-tab reconnects still work because
  Session.disconnect() sets __conn = None before any reconnect attempt.
• No documentation changes needed.

Summary by Sourcery

Bug Fixes:

• Reject reuse of an existing session if its connection is still active, ensuring duplicated browser tabs receive separate sessions and do not interfere with each other.

[CLAassistant]

All committers have signed the CLA.

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