feat(org): add team visibility so org members can discover teams (#37680)

Closes #37670.

Today, org members in Gitea only see teams they're a member of. In
larger orgs that hurts onboarding and discoverability — there's no way
to look up which team owns what without asking around. GitHub solves
this with a per-team visibility setting; this PR brings the same model
to Gitea.

## What changes

- Every team gets a `visibility` setting:
- `private` *(default)* — only team members and org owners can see the
team. Same as today's behavior.
- `limited` — listable by any member of the organization. Members and
the repos the team has access to are visible too. Non-org-members still
see nothing.
  - `public` — listable by any signed-in user.
- The Owners team visibility is fixed and cannot be changed via
settings.
- Existing teams default to `private`, so this is a no-op for anyone who
doesn't change anything.

## API

- `Team`, `CreateTeamOption`, `EditTeamOption` all gain a `visibility`
field (string enum: `private` | `limited` | `public`).
- `GET /orgs/{org}/teams` and `/orgs/{org}/teams/search` now apply the
same visibility rules as the web UI:
  - site admins and org owners still see every team
- other org members see their own teams plus any `limited` or `public`
team
  - `private` teams are no longer leaked through these endpoints
- Swagger/OpenAPI specs regenerated.

## UI

View from admin2 (not an owner):
<img width="1669" height="726"
src="https://github.com/user-attachments/assets/daf4bccb-644b-4426-b178-71963aeaf73b"
/>

View from admin (owner):

<img width="2559" height="863"
src="https://github.com/user-attachments/assets/4f22cebc-e9df-4fd2-8ed4-724d31fadb7a"
/>

---------

Signed-off-by: bircni <bircni@icloud.com>
Co-authored-by: TheFox0x7 <thefox0x7@gmail.com>
Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>

modules/structs/org_team.go

@@ -4,6 +4,20 @@
 
 package structs
 
+// TeamVisibility controls who can list a team within its organization.
+//   - "public":  visible to any signed-in user (still bounded by org visibility)
+//   - "limited": visible to any member of the parent organization
+//   - "private": visible only to team members and org owners
+//
+// swagger:enum TeamVisibility
+type TeamVisibility string
+
+const (
+	TeamVisibilityPublic  TeamVisibility = "public"
+	TeamVisibilityLimited TeamVisibility = "limited"
+	TeamVisibilityPrivate TeamVisibility = "private"
+)
+
 // Team represents a team in an organization
 type Team struct {
 	// The unique identifier of the team
@@ -24,6 +38,11 @@ type Team struct {
 	UnitsMap map[string]string `json:"units_map"`
 	// Whether the team can create repositories in the organization
 	CanCreateOrgRepo bool `json:"can_create_org_repo"`
+	// Team visibility within the organization. "private" teams are only
+	// listable by members and org owners; "limited" teams are listable by
+	// any organization member; "public" teams are listable by any signed-in
+	// user.
+	Visibility TeamVisibility `json:"visibility"`
 }
 
 // CreateTeamOption options for creating a team
@@ -42,6 +61,8 @@ type CreateTeamOption struct {
 	UnitsMap map[string]string `json:"units_map"`
 	// Whether the team can create repositories in the organization
 	CanCreateOrgRepo bool `json:"can_create_org_repo"`
+	// Team visibility within the organization. Defaults to "private".
+	Visibility TeamVisibility `json:"visibility" binding:"OmitEmpty;In(public,limited,private)"`
 }
 
 // EditTeamOption options for editing a team
@@ -60,4 +81,7 @@ type EditTeamOption struct {
 	UnitsMap map[string]string `json:"units_map"`
 	// Whether the team can create repositories in the organization
 	CanCreateOrgRepo *bool `json:"can_create_org_repo"`
+	// Team visibility within the organization. When omitted, visibility is
+	// left unchanged.
+	Visibility *TeamVisibility `json:"visibility" binding:"OmitEmpty;In(public,limited,private)"`
 }