[feature]: Google Calendar Integration – Sync Work Items, Cycles & Due Dates

Is there an existing issue for this? • I have searched the existing issues Summary Summary Plane currently lacks a native Google Calendar integration. Teams that use Plane for project management and Google Calendar for scheduling have no built-in way to see their work items, cycle timelines, or due dates reflected on their calendar — forcing them to either maintain both manually or rely on third-party automation tools like Zapier or n8n. This feature request proposes a native Google Calendar sync as a workspace-level integration in Plane, similar to how Linear and ClickUp have approached this problem. Proposed Behavior When enabled, the integration should support: • Work Items → Calendar Events: Any work item with a due date (and optionally a start date) should be synced as a Google Calendar event, with the assignee's calendar updated accordingly. • Cycle Sync: Active and upcoming Cycles should be synced as multi-day calendar blocks, giving teams a timeline …