Unfortunately, simply setting up the QGIS cache (see this guide if you don’t know how) won’t cause caching of plain WMS responses (no matter what that guide says!), whereas WMTS or XYZ servers do get cached. This can be seen by using the “Debugging/Development Tools” panel to monitor network activity.
The reason for this is that the extent which is in view in QGIS determines the WMS response image coverage, so unless you are at exactly the same position and scale, there will be no “hit” on the cache.
The answer is to add the WMS layer using the “Data Source Manager” (shortcut Ctrl-L), rather than from the “Browser”. This offers you the option to set the tile size (width and height) to use. Choose a layer then “Add”. NB: once added, it doesn’t seem possible to change the tile size. This forces requests to discrete tiles, with 1 request for each. Now, so long as you do not change scale, panning back-and-forth will cause QGIS to pick up the cached tiles even if you don’t pan back to the same place, since the tile boundaries are defined in spatial coordinates.
I used a tile size of 500×500 with some hillshade based on 1m spatial resolution Lidar. Small tile sizes are not a good idea as the network latency will kill the performance on first load (this can be used to show that caching is working, e.g. use a tile size of 100×100 clearly shows the 1st load performance contrasted to the use of cached tiles).