What does this PR do?

Fixes a long-standing UX gap: team admins could not invite people who weren’t already team members from the event type Assignment tab. They had to leave the event type editor, go to Settings → Teams → Members, invite the person there, wait for them to accept, and then come back to assign them. This PR removes that friction entirely.

A new “Invite people by email” section is added below the existing host assignment UI. It allows admins to type one or multiple email addresses (comma/space/semicolon separated), validate them, and send invites — all without leaving the Assignment tab.

• Fixes #13532
• Fixes CAL-3076
• /claim #13532

Approach

Rather than modifying the existing CheckedTeamSelect dropdown (which carries risk of breaking the existing assignment flow), this PR adds a self-contained InviteByEmailSection component rendered inside AddMembersWithSwitchWebWrapper. This keeps concerns separated and the existing host selection logic untouched.

The invite reuses the existing viewer.teams.inviteMember tRPC procedure — no new backend changes required. After a successful invite, onInvited invalidates viewer.teams.get and viewer.eventTypes.get so the UI refetches automatically.

Root cause of PR #28354 being closed

PR #28354 was previously closed because of a dead code bug — the original return <AddMembersWithSwitch {...props} /> statement was never removed when InviteByEmailSection was added, making the new component completely unreachable. This PR fixes that by restructuring the component correctly.

Key changes

• AddMembersWithSwitchWebWrapper.tsx — removed the early return that blocked InviteByEmailSection from ever rendering; added the InviteByEmailSection component with email parsing, validation, loading state, and cache invalidation on success
• packages/i18n/locales/en/common.json — added 3 i18n keys:
  • invite_team_member_by_email
  • invite_team_member_by_email_description
  • invite_team_member_email_placeholder

Visual Demo

🎥 Before — no invite option exists on the Assignment tab: https://www.loom.com/share/29d3a972ac2e40c6827849302acb6258

✅ After — invite section visible, invites sent, pending badge appears in Settings: https://www.loom.com/share/3bac8f7f9a0541c2b86e84462d17f45c

After screenshot — invited members appear as Pending in Settings → Teams → Members:

[![Pending invites] ]

How should this be tested?

No special environment variables required. Use any local cal.com dev setup with a team.

Minimal test data:

• A user who is the owner of a team
• A Round Robin team event type

Happy path:

1. Create a team or use an existing one
2. Create or open a Round Robin team event type
3. Go to the Assignment tab
4. Scroll below the host selector — you should see “Invite people by email”
5. Type one or more emails (e.g. test@example.com, test2@example.com)
6. Click Invite or press Enter
7. ✅ A success toast appears and the input clears
8. Go to Settings → Teams → [Your Team] → Members
9. ✅ The invited email(s) appear with a Pending badge

Mandatory Tasks

• I have self-reviewed the code
• I have updated the developer docs in /docs if this PR makes changes that would require a documentation change. N/A — UI-only addition using existing backend procedure.
• I confirm automated tests are in place that prove my fix is effective or that my feature works.

Checklist

• I have read the contributing guide
• My code follows the style guidelines of this project
• I have commented my code, particularly in hard-to-understand areas
• I have checked if my changes generate no new warnings