I still don't understand why Atlassian "locked" the "Team" field and made it so complicated to use, but that's besides the point.
I am working on automation to create an issue in a project with the mandatory "Team" field, when some workflow transition happens in another project. The project field doesn't show on the list of the available fields in "Choose fields..." drop-down:

Is there another option (JSON?) to do so, similar to a cascading select list? I'd greatly appreciate community's help. Please let me know if you have any questions.
I've tried the below JSON option, but it doesn't work:
{
"update": {
"customfield_13600": [
{
"set": {
"value": "{{triggerIssue.fields.customfield_13600.value}}"
}
}
]
}
}