As frustrating as it is, I think it's default behaviour in MacOS, so that might explain why it's happening in Affinity and why it perhaps (I don't really know, I've never tried to write any software!) isn't as simple a fix as we think it is.
I've experimented with some of Apple's own software such as Apple Pages and Apple Numbers. What appears to happen is the file browser that appears in dialogs (such as when you use File > Open or File > Save ie. not the main file browser you use on the desktop finder) remembers it's last state, so the next time you perform any action that uses that dialog file browser (whether that is Open, Save or Export) it will still be in the last place you left it.
The problem seems to arise if you open a file from the desktop finder, or the Recents menu or any other "shortcut" method that doesn't use the dialog file browser. None of these other methods update the dialog file browser's state and so the next time you go to Open, Save or Export it will still be in whatever folder you last opened, saved or exported to/from through the dialog file browser.
There probably is a way that Affinity can work around this (as I assume Adobe have) to get the behaviour we want, but perhaps a feature request to Apple would be in order as well so that we can get this as the default behaviour across all software without the software developers have to work around it!