Steps to reproduce 🕹

Link to live example: https://codesandbox.io/s/tender-shannon-2o3hv7

https://www.loom.com/share/eb4bd147cdb043139c30a055f0f9f842

Browser - Chrome, Firefox

• Case 1
  Steps:

1. Click on the filter button on the data grid toolbar,
2. Then, click on the start text field/ end text field of the date range picker

• Case 2
  Steps:

1. Click on the column button on the data grid toolbar,
2. Then, click on the start text field/ end text field of the date range picker

Current behavior 😯

Opening the date range picker after the filter panel or column panel closes the date range picker automatically for the first time.

But this doesn't happens when density menu appears and date range picker is being opened

Expected behavior 🤔

Opening the date range picker after the filter panel or column panel should not close the date range picker automatically. It should behave the same way as when we toggle between different panels like filter, column, density, etc.

Context 🔦

I need to add a date range filter which is not related to the columns of the data grid. So inorder to achieve that i am using the date range picker component and placing it in the data grid toolbar.

Your environment 🌎

System:
    OS: macOS 12.6.1
  Binaries:
    Node: 18.10.0 - ~/.nvm/versions/node/v18.10.0/bin/node
    Yarn: 1.22.19 - /opt/homebrew/bin/yarn
    npm: 8.19.2 - ~/.nvm/versions/node/v18.10.0/bin/npm
  Browsers:
    Chrome: 106.0.5249.119
    Edge: Not Found
    Firefox: 106.0.5
    Safari: 16.1
  npmPackages:
    @emotion/react: ^11.10.4 => 11.10.5 
    @emotion/styled: ^11.10.4 => 11.10.5 
    @mui/base:  5.0.0-alpha.103 
    @mui/core-downloads-tracker:  5.10.11 
    @mui/icons-material: ^5.10.6 => 5.10.9 
    @mui/material: ^5.10.6 => 5.10.11 
    @mui/private-theming:  5.10.9 
    @mui/styled-engine:  5.10.8 
    @mui/system:  5.10.10 
    @mui/types:  7.2.0 
    @mui/utils:  5.10.9 
    @mui/x-data-grid:  5.17.8 
    @mui/x-data-grid-pro: ^5.17.4 => 5.17.8 
    @mui/x-date-pickers:  5.0.9 
    @mui/x-date-pickers-pro: ^5.0.9 => 5.0.9 
    @mui/x-license-pro:  5.17.0 
    @types/react: ^18.0.20 => 18.0.24 
    react: ^18.2.0 => 18.2.0 
    react-dom: ^18.2.0 => 18.2.0 
    typescript: ^4.8.3 => 4.8.4 

Order ID 💳 (optional)

No response