Is it normal for bluetooth devices to stop responding when CPU is too busy?

Since I can not pinpoint your BT problem ... I suggest you try this great tool provided by Apple.

You have to download Bluetooth Explorer as part of the 'Additional Tools for Xcode' package that's available (registration required) at https://developer.apple.com/download/more/.

Go to that link, then search for 'Additional', and find the Additional Tools package for the latest version of Xcode (you don't actually need Xcode installed to use the Bluetooth Explorer app!).

Among other tools available, Open the Hardware Folder and select the BT Explorer.

Use it to determine your BT performance while you are running the IntelliJ IDEA.