Is there a way to recover the home directory from a previous Fedora 40 install that fails to boot?
Welcome to Fedora @airjouster45
yes.
Start live iso, open Files if Gnome and change to the section “other locations” and you might find there the mounted disks form your compter. Backup your files 
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Added f40, file-recovery, selinux, system-recovery
You can boot the system by disabling SELinux in GRUB with certain kernel parameters and then restore SELinux labels as explained here:
Chapter 2. Changing SELinux states and modes | Red Hat Product Documentation