Since browser cache is keyed by window location its still possible to do a cache probing attack by timing navigation.
It does not matter if the navigation initiator is cross-site. (Navigations | XS-Leaks Wiki)
This allows a cache based XS-Search on websites when same-site resources are used based on the search query controlled by the attacker.
Cache probing tool: https://sites.google.com/view/xsleaks
Old cache probing attacks: https://github.com/NDevTK/CacheAttack
A fix is being planned in https://groups.google.com/a/chromium.org/g/blink-dev/c/YpxpzceGw68/m/ezbYJOSeAAAJ