Update

curl --request PUT \
  --url https://api.incident.io/v2/schedules/{schedule_id}/sync_rules/{id} \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "annotations": {
    "incident.io/terraform/version": "3.0.0"
  },
  "sync_type": "on_call"
}
'

import requests

url = "https://api.incident.io/v2/schedules/{schedule_id}/sync_rules/{id}"

payload = {
    "annotations": { "incident.io/terraform/version": "3.0.0" },
    "sync_type": "on_call"
}
headers = {
    "Authorization": "Bearer <token>",
    "Content-Type": "application/json"
}

response = requests.put(url, json=payload, headers=headers)

print(response.text)

const options = {
  method: 'PUT',
  headers: {Authorization: 'Bearer <token>', 'Content-Type': 'application/json'},
  body: JSON.stringify({annotations: {'incident.io/terraform/version': '3.0.0'}, sync_type: 'on_call'})
};

fetch('https://api.incident.io/v2/schedules/{schedule_id}/sync_rules/{id}', options)
  .then(res => res.json())
  .then(res => console.log(res))
  .catch(err => console.error(err));

<?php

$curl = curl_init();

curl_setopt_array($curl, [
  CURLOPT_URL => "https://api.incident.io/v2/schedules/{schedule_id}/sync_rules/{id}",
  CURLOPT_RETURNTRANSFER => true,
  CURLOPT_ENCODING => "",
  CURLOPT_MAXREDIRS => 10,
  CURLOPT_TIMEOUT => 30,
  CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
  CURLOPT_CUSTOMREQUEST => "PUT",
  CURLOPT_POSTFIELDS => json_encode([
    'annotations' => [
        'incident.io/terraform/version' => '3.0.0'
    ],
    'sync_type' => 'on_call'
  ]),
  CURLOPT_HTTPHEADER => [
    "Authorization: Bearer <token>",
    "Content-Type: application/json"
  ],
]);

$response = curl_exec($curl);
$err = curl_error($curl);

curl_close($curl);

if ($err) {
  echo "cURL Error #:" . $err;
} else {
  echo $response;
}

package main

import (
	"fmt"
	"strings"
	"net/http"
	"io"
)

func main() {

	url := "https://api.incident.io/v2/schedules/{schedule_id}/sync_rules/{id}"

	payload := strings.NewReader("{\n  \"annotations\": {\n    \"incident.io/terraform/version\": \"3.0.0\"\n  },\n  \"sync_type\": \"on_call\"\n}")

	req, _ := http.NewRequest("PUT", url, payload)

	req.Header.Add("Authorization", "Bearer <token>")
	req.Header.Add("Content-Type", "application/json")

	res, _ := http.DefaultClient.Do(req)

	defer res.Body.Close()
	body, _ := io.ReadAll(res.Body)

	fmt.Println(string(body))

}

HttpResponse<String> response = Unirest.put("https://api.incident.io/v2/schedules/{schedule_id}/sync_rules/{id}")
  .header("Authorization", "Bearer <token>")
  .header("Content-Type", "application/json")
  .body("{\n  \"annotations\": {\n    \"incident.io/terraform/version\": \"3.0.0\"\n  },\n  \"sync_type\": \"on_call\"\n}")
  .asString();

require 'uri'
require 'net/http'

url = URI("https://api.incident.io/v2/schedules/{schedule_id}/sync_rules/{id}")

http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true

request = Net::HTTP::Put.new(url)
request["Authorization"] = 'Bearer <token>'
request["Content-Type"] = 'application/json'
request.body = "{\n  \"annotations\": {\n    \"incident.io/terraform/version\": \"3.0.0\"\n  },\n  \"sync_type\": \"on_call\"\n}"

response = http.request(request)
puts response.read_body

{
  "schedule_sync_rule": {
    "created_at": "2021-08-17T13:28:57.801578Z",
    "id": "01JXYZ000000000000000000CD",
    "rotation_id": "01JXYZ000000000000000000RT",
    "schedule_id": "01JXYZ000000000000000000EF",
    "schedule_sync_target": {
      "add_bot_to_group": true,
      "created_at": "2021-08-17T13:28:57.801578Z",
      "id": "01JXYZ000000000000000000AB",
      "linked_schedules": [
        {
          "id": "01G0J1EXE7AXZ2C93K61WBPYEH",
          "name": "Primary On-Call Schedule",
          "team_ids": [
            "01JPQA75EPNEES4479P16P4XAB"
          ]
        }
      ],
      "slack_team_id": "T02A1AZHG3J",
      "slack_user_group_id": "S06MNNU5BMK",
      "updated_at": "2021-08-17T13:28:57.801578Z"
    },
    "schedule_sync_target_id": "01JXYZ000000000000000000AB",
    "sync_type": "on_call",
    "updated_at": "2021-08-17T13:28:57.801578Z"
  }
}