Add Activepieces integration for workflow automation

- Add Activepieces fork with SmoothSchedule custom piece
- Create integrations app with Activepieces service layer
- Add embed token endpoint for iframe integration
- Create Automations page with embedded workflow builder
- Add sidebar visibility fix for embed mode
- Add list inactive customers endpoint to Public API
- Include SmoothSchedule triggers: event created/updated/cancelled
- Include SmoothSchedule actions: create/update/cancel events, list resources/services/customers

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

activepieces-fork/packages/shared/src/lib/flows/operations/add-branch.ts

@@ -0,0 +1,26 @@
+import { insertAt } from '../../common'
+import { FlowActionType, RouterAction } from '../actions/action'
+import { FlowVersion } from '../flow-version'
+import { flowStructureUtil } from '../util/flow-structure-util'
+import { AddBranchRequest } from '.'
+
+
+function _addBranch(flowVersion: FlowVersion, request: AddBranchRequest): FlowVersion {
+    return flowStructureUtil.transferFlow(flowVersion, (parentStep) => {
+        if (parentStep.name !== request.stepName || parentStep.type !== FlowActionType.ROUTER) {
+            return parentStep
+        }
+        const routerAction = parentStep as RouterAction
+        return {
+            ...routerAction,
+            settings: {
+                ...routerAction.settings,
+                branches: insertAt(routerAction.settings.branches, request.branchIndex, flowStructureUtil.createBranch(request.branchName, request.conditions)),
+            },
+            children: insertAt(routerAction.children, request.branchIndex, null),
+        }
+    })
+}
+
+
+export { _addBranch }