OverlayPanel: After interaction two mouse clicks are needed to close dialog

Describe the bug

When a button inside an OverlayPanel is clicked, two clicks outside of the dialog are necessary to close the dialog. If no interaction inside the dialog has happened, the dialog can be closed with a single mouse click.

Reproducer

https://stackblitz.com/edit/kt8tihbc

System Information

System:
    OS: Linux 7.0 Fedora Linux 43 (Workstation Edition)
    CPU: (24) x64 12th Gen Intel(R) Core(TM) i9-12900K
    Memory: 66.42 GB / 125.46 GB
    Container: Yes
    Shell: 5.3.0 - /bin/bash
  Binaries:
    Node: 22.22.2 - /usr/bin/node
    Yarn: 4.15.0 - /usr/local/bin/yarn
    npm: 10.3.0 - /usr/local/bin/npm
    bun: 1.1.4 - /usr/local/bin/bun
  Browsers:
    Chrome: 148.0.7778.178
    Firefox: 151.0.1
    Firefox Developer Edition: 151.0.1

Steps to reproduce the behavior

1. Open OverlayDialog
2. Click a button inside the dialog, e.g. pagination button
3. Click outside the dialog - the dialog should be closed but is not
4. Click again outside the dialog - the dialog will be closed

Expected behavior

The dialog should be closed on the first click outside of the dialog.

Start by reproducing the behavior in the linked StackBlitz example and then trace the OverlayPanel entry point and its outside-click handling after an internal button interaction. Done means the first click outside the dialog closes it, with the existing interaction behavior preserved.