fix: Unify public-only token filtering in API queries and repo access checks (#37118) (#37773)

backport #37118 

This PR closes remaining `public-only` token gaps in the API by making
the restriction apply consistently across repository, organization,
activity, notification, and authenticated `/api/v1/user/...` routes.

Previously, `public-only` tokens were still able to:
- receive private results from some list/search/self endpoints,
- access repository data through ID-based lookups,
- and reach several authenticated self routes that should remain
unavailable for public-only access.

This change treats `public-only` as a cross-cutting visibility boundary:
- list/search endpoints now filter private resources consistently,
- repository lookups enforce the same restriction even when addressed
indirectly,
- and self routes that inherently expose or mutate private account state
now reject `public-only` tokens.

---
Generated by a coding agent with Codex 5.2

Co-authored-by: silverwind <me@silverwind.io>
Co-authored-by: Claude (Opus 4.7) <noreply@anthropic.com>
Co-authored-by: Nicolas <bircni@icloud.com>

tests/integration/api_user_star_test.go

@@ -17,6 +17,7 @@ import (
 	"code.gitea.io/gitea/tests"
 
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
 )
 
 func TestAPIStar(t *testing.T) {
@@ -155,3 +156,24 @@ func TestAPIStarDisabled(t *testing.T) {
 		MakeRequest(t, req, http.StatusForbidden)
 	})
 }
+
+func TestAPIStarPublicOnly(t *testing.T) {
+	defer tests.PrepareTestEnv(t)()
+
+	token := getUserToken(t, "user2", auth_model.AccessTokenScopeReadUser, auth_model.AccessTokenScopeReadRepository, auth_model.AccessTokenScopePublicOnly)
+	req := NewRequest(t, "GET", "/api/v1/user/starred").
+		AddTokenAuth(token)
+	resp := MakeRequest(t, req, http.StatusOK)
+
+	repos := DecodeJSON(t, resp, []api.Repository{})
+	if assert.Len(t, repos, 1) {
+		assert.Equal(t, "user5/repo4", repos[0].FullName)
+	}
+
+	req = NewRequest(t, "GET", "/api/v1/users/user2/starred").
+		AddTokenAuth(token)
+	resp = MakeRequest(t, req, http.StatusOK)
+	repos = DecodeJSON(t, resp, []api.Repository{})
+	require.Len(t, repos, 1)
+	assert.Equal(t, "user5/repo4", repos[0].FullName)
+}