Frontend Layout Issue in TYPO3 v13: Incorrect Template Rendering After Cache Clear

# Bug Report

## Description

While updating a website from TYPO3 v12 to v13, I noticed that sometimes the correct template is not active in the frontend. For example, the backend is set to use a three-column layout, but after clearing the cache, the default template is applied in the frontend. This results in only the middle section being visible, with the columns missing. After multiple reloads and navigating back and forth, it usually displays correctly.

## Steps to Reproduce

- Update a TYPO3 website from v12 to v13, or set up a new TYPO3 v13.4 project using DDEV with the latest Bootstrap package (v15.0) installed.
- In the TYPO3 backend, configure a page to use a multi-column layout (e.g., a three-column or two-column layout).
- Clear the cache.
- Open the page in the frontend.

### Expected behavior

I expected the frontend to consistently display the layout configured in the backend, regardless of cache clearing. The chosen template (e.g., three-column or two-column layout) should reliably render as set in the backend without requiring reloads or navigation.

### Actual behavior

Instead, after clearing the cache, the frontend often defaults to the basic template, displaying only the middle section without the configured columns. Multiple reloads or navigating between pages are sometimes required for the correct layout to appear as set in the backend.

### Screenshots

https://share.cleanshot.com/fhty8j6m (Video)

## Versions

typo3/cms-base-distribution:^13.4
bk2k/bootstrap-package:^15.0

Start by reproducing the frontend rendering problem in a TYPO3 v13.4 project with bk2k/bootstrap-package v15.0, using DDEV if following the report, and clear the cache before loading a configured two- or three-column page. Compare the backend layout selection with the rendered frontend and verify that the configured columns appear consistently after reloads; the payload names no source file or test.

Written by the indexing model from the issue text.