feat: add create invite link endpoint (#24073)

* feat: add create invite link endpoint

* tests: add e2e test

* chore: feeback

* chore: feeback

* chore; udate summary

* chore; udate summary

* chore: deelte swagger

docs/api-reference/v2/openapi.json

@@ -4421,6 +4421,70 @@
         "tags": ["Orgs / Teams / Event Types / Private Links"]
       }
     },
+    "/v2/organizations/{orgId}/teams/{teamId}/invite": {
+      "post": {
+        "operationId": "OrganizationsTeamsInviteController_createInvite",
+        "summary": "Create team invite link",
+        "parameters": [
+          {
+            "name": "Authorization",
+            "in": "header",
+            "description": "For non-platform customers - value must be `Bearer <token>` where `<token>` is api key prefixed with cal_",
+            "required": false,
+            "schema": {
+              "type": "string"
+            }
+          },
+          {
+            "name": "x-cal-secret-key",
+            "in": "header",
+            "description": "For platform customers - OAuth client secret key",
+            "required": false,
+            "schema": {
+              "type": "string"
+            }
+          },
+          {
+            "name": "x-cal-client-id",
+            "in": "header",
+            "description": "For platform customers - OAuth client ID",
+            "required": false,
+            "schema": {
+              "type": "string"
+            }
+          },
+          {
+            "name": "orgId",
+            "required": true,
+            "in": "path",
+            "schema": {
+              "type": "number"
+            }
+          },
+          {
+            "name": "teamId",
+            "required": true,
+            "in": "path",
+            "schema": {
+              "type": "number"
+            }
+          }
+        ],
+        "responses": {
+          "200": {
+            "description": "",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/CreateInviteOutputDto"
+                }
+              }
+            }
+          }
+        },
+        "tags": ["Orgs / Teams / Invite"]
+      }
+    },
     "/v2/organizations/{orgId}/teams/{teamId}/memberships": {
       "get": {
         "operationId": "OrganizationsTeamsMembershipsController_getAllOrgTeamMemberships",
@@ -19915,6 +19979,35 @@
         },
         "required": ["userId", "role"]
       },
+      "InviteDataDto": {
+        "type": "object",
+        "properties": {
+          "token": {
+            "type": "string",
+            "description": "Unique invitation token for this team. Share this token with prospective members to allow them to join the team/organization.",
+            "example": "f6a5c8b1d2e34c7f90a1b2c3d4e5f6a5b7c8d9e0f1a2b3c4d5e6f7a8b9c0d1e2"
+          },
+          "inviteLink": {
+            "type": "string",
+            "description": "Complete invitation URL that can be shared with prospective members. Opens the signup page with the token and redirects to getting started after signup.",
+            "example": "http://app.cal.com/signup?token=f6a5c8b1d2e34c7f90a1b2c3d4e5f6a5b7c8d9e0f1a2b3c4d5e6f7a8b9c0d1e2&callbackUrl=/getting-started"
+          }
+        },
+        "required": ["token", "inviteLink"]
+      },
+      "CreateInviteOutputDto": {
+        "type": "object",
+        "properties": {
+          "status": {
+            "type": "string",
+            "example": "success"
+          },
+          "data": {
+            "$ref": "#/components/schemas/InviteDataDto"
+          }
+        },
+        "required": ["status", "data"]
+      },
       "Attribute": {
         "type": "object",
         "properties": {