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_issue_test.go

@@ -108,7 +108,7 @@ func testAPIListIssuesPublicOnly(t *testing.T) {
 
 	publicOnlyToken := getTokenForLoggedInUser(t, session, auth_model.AccessTokenScopeReadIssue, auth_model.AccessTokenScopePublicOnly)
 	req = NewRequest(t, "GET", link.String()).AddTokenAuth(publicOnlyToken)
-	MakeRequest(t, req, http.StatusForbidden)
+	MakeRequest(t, req, http.StatusNotFound)
 }
 
 func testAPICreateIssue(t *testing.T) {