Boost: Fix page cache e2e tests (#39695)

* Fix not always logged in for page cache e2e test

This allows the page cache e2e test to be run independently every time
without issues.

* Use WP_Filesystem when trying to update wp-config.php for pace cache

* add changelog

* Use WP_Filesystem_Direct to update wp-config.php

* Set file permissions to avoid fatal errors

* Update param value

* Rename method

Committed via a GitHub action: https://github.com/Automattic/jetpack/actions/runs/11272670639

Upstream-Ref: Automattic/jetpack@4e82c59