For future note, I found this worked:
let x = {
"linkedPulseIds": [{
"linkedPulseId": 2643558944
}]
}
let mutation = `mutation {
change_column_value(board_id: 2588471113,
item_id: 2643558945,
column_id: "connect_boards30",
value: ${JSON.stringify(JSON.stringify(x))}) {
id
}
}
Got it from here: Parsing Error: No error on playground, error in JavaScript