Rename / Overwrite sometimes fails

new bug with the rename & overwrite check. If you do something like:

1. Delete xyz.
2. Rename abc to xyz

DA will do a HEAD request to check for xyz existence to prevent overwrites and if you're in a normal browsing context (no console open / no cache), the browser use its existing cache and say, "sorry, this page does exist." even when it doesn't We need the fetch to bypass the default browser cache.

From [slack convo](https://adobe-dx-support.slack.com/archives/C06HHBGPWMD/p1776793710669129?thread_ts=1776274320.627189&cid=C06HHBGPWMD)

Start by locating the rename/overwrite flow and the HEAD request used to check whether the destination exists. Reproduce the delete-then-rename sequence in a normal browsing context without the console or cache controls, then verify that the existence check bypasses the browser cache and does not report the deleted page as present.

Written by the indexing model from the issue text.