Low-maintenance path
Create a small Apps Script web app that receives the InstaChime outgoing webhook and appends a row. This avoids storing Google OAuth tokens inside InstaChime while keeping the destination under your Google Workspace account.
function doPost(e) {
var payload = JSON.parse(e.postData.contents);
var lead = payload.lead || payload;
var sheet = SpreadsheetApp.openById("SPREADSHEET_ID").getSheetByName("Leads");
sheet.appendRow([
new Date(),
lead.customer_name || "",
lead.email || "",
lead.phone || "",
lead.source || "",
lead.message || ""
]);
return ContentService.createTextOutput("ok");
}