Hello @qw2 ,
First let me thank you for posting.
Before checking the connection, you should set the connection parameters for STM32CubeIDE:
Go to [Window]>[Preferences]>[General]>Network connections]

Change [Active provider] to Manual.
Update the proxy entries for HTTP and HTTPS with specific HOST, Port, User, and Password using the [Edit...] button.
Then, go to [Window]>[Preferences]>[STM32Cube]>[Firmware Updater] and click on the "Check connection" button.

For more details, check the STM32CubeIDE user manual UM2609 section 1.5.3 Preferences - Network proxy settings.
Thanks.
Mahmoud