When starting a debug session in VSCode it will try to attach itself to the Unity process. It does this by looking for a process named "Unity Editor". However, when simultaneously running the Unity Hub application it will find multiple such processes and won't start.

Output from VSCode:

UnityDebug: Searching for Unity process 'Unity Editor'
UnityDebug: Multiple targets with name 'Unity Editor' running. Unable to connect
UnityDebug: Found Unity process 'Unity Editor (Unity)' (9033)
UnityDebug: Found Unity process 'Unity Editor (Unity Hub Helper)' (9014)
UnityDebug: Found Unity process 'Unity Editor (Unity Hub Helper)' (8994)
UnityDebug: Found Unity process 'Unity Editor (Unity Hub)' (8993)

Fixed by Unity Debugger extension update.
Version 1.3.0 of the Unity Debugger for VSCode has now been published which fixes this issue:
https://marketplace.visualstudio.com/items?itemName=Unity.unity-debug