UPDATE 2
Now the new tab shows directly a selection mode that says:
Select a language to get started. Start typing to dismiss, or don't show this again.
So you just need to press Select a language

UPDATE 1
In the bottom right corner is available the Select Language Mode functionality that now let you select a formatting option, the default one is Plain Text. The same functionality can be used with Ctrl + KM or by selecting Change Language Mode from the command palette.

OLD ANSWER
I found two solutions to this specific problem, even if they seems more a workaround than a proper solution:
- Using a specific extension to format particular code (json or xml)
- Trick VSCode into thinking default unsaved files are json
1 Extensions that format as specific code
Install specific extension that add language specific commands:
- XML Tools
default keybinding Ctrl + Shift + Alt + B
- JSON Tools
default keybinding Ctrl + Alt + M
PRO
- no default settings are changed
- specific format can be used on any selection in any file
- it's the same solution that notepad++ implement
CONS
- additional extensions to download may look overkill only to format something
- more keybindings and additional non standard behaviours
2 VSCode default unsaved files trick
Add a configuration to settings.json that specify json as the type of document for untitled files:
"files.associations": {
"Untitled-*" : "json"
}
PRO
- default Format document is used
- no additional download is required
CONS
- only one format can be specified
- locale-dependant (in languages other than English it should not work)