refactor: extract helper functions from SearchIssues (#36158)

## Summary

This PR refactors the `SearchIssues` function in
`routers/api/v1/repo/issue.go` by extracting common logic into reusable
helper functions:

- `parseIssueIsClosed()`: Parses the "state" query parameter and returns
the corresponding `isClosed` option
- `parseIssueIsPull()`: Parses the "type" query parameter and returns
the corresponding `isPull` option
- `buildSearchIssuesRepoIDs()`: Builds the list of repository IDs for
issue search based on query parameters

### Benefits:
- Improved code readability
- Smaller, more focused functions
- Easier to test individual components
- Potential for reuse in other handlers

### Changes:
- Extracted 3 helper functions from the ~292 line `SearchIssues`
function
- No functional changes - behavior remains the same
- Proper error handling preserved

## Test plan
- [ ] Verify existing API tests pass
- [ ] Manual testing of `/repos/issues/search` endpoint

Ref: #35015

---------

Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>

tests/integration/api_issue_test.go

@@ -19,6 +19,7 @@ import (
 	user_model "code.gitea.io/gitea/models/user"
 	"code.gitea.io/gitea/modules/setting"
 	api "code.gitea.io/gitea/modules/structs"
+	"code.gitea.io/gitea/modules/test"
 	"code.gitea.io/gitea/tests"
 
 	"github.com/stretchr/testify/assert"
@@ -264,9 +265,8 @@ func TestAPIEditIssue(t *testing.T) {
 
 func TestAPISearchIssues(t *testing.T) {
 	defer tests.PrepareTestEnv(t)()
-
-	// as this API was used in the frontend, it uses UI page size
-	expectedIssueCount := min(20, setting.UI.IssuePagingNum) // 20 is from the fixtures
+	defer test.MockVariableValue(&setting.API.DefaultPagingNum, 20)()
+	expectedIssueCount := 20 // 20 is from the fixtures
 
 	link, _ := url.Parse("/api/v1/repos/issues/search")
 	token := getUserToken(t, "user1", auth_model.AccessTokenScopeReadIssue)