There are two problems that you are encountering here.
The first problem is update or fields should be provided separately to Jira's edit issue API, not one inside of the other. They have equivalent functionality so normally only one is used. For example to update the summary field provide either update:
{
"update": {
"summary": [
{
"set": "Updated by update"
}
]
}
}
or fields:
{
"fields": {
"summary": "Summary set by fields"
}
}
However the status field is a special case and can't be updated directly, which is the second problem here. Changing a status in Jira is called a transition. You need to trigger the transition to move the issue into the status you want.
Start by identifying the available transitions by calling the get transitions API:
GET https://example.net/rest/api/latest/issue/PID-XX/transitions
This tells you which transitions are currently available, something like this:
{
"expand": "transitions",
"transitions": [
{
"id": "21",
"name": "Fixed",
"to": {
"self": "https://example.net/rest/api/2/status/10001",
"description": "",
"iconUrl": "https://example.net/images/icons/status_generic.gif",
"name": "Fixed",
"id": "10001",
"statusCategory": {
"self": "https://example.net/rest/api/2/statuscategory/3",
"id": 3,
"key": "done",
"colorName": "green",
"name": "Done"
}
}
}
]
}
Take the id of the transition you want, in this case 21, then post it to the issue transition API:
POST https://example.net/rest/api/latest/issue/PID-XX/transitions
Use a request body like this:
{
"transition": {
"id": 21
}
}
You should get a 204 HTTP response from Jira which indicates the transition was successful.