It seems this is a known bug in Fedora 34 with the KDE/Plasma spin:

https://bugzilla.redhat.com/show_bug.cgi?id=1953472

As of today, the workarounds that seem to work are these:

1. After logging in, open a command shell and manually invoke program vmware-user-suid-wrapper
   OR
2. Follow Rex Dieter's advice in Comment 4 of the Bugzilla bug report (#1953472) mentioned above, i.e.,

* edit /etc/xdg/startkderc, set systemdBoot=false
* log out
* when logging in to plasma, choose x11 session type (instead of wayland)

Either of these two methods ensures the logged-in user has the required vmtoolsd process:

$ ps aux | grep vmtoolsd
someuser+ 17188 2.7 0.8 507108 35332 pts/1 Sl 19:20 0:00 /usr/bin/vmtoolsd -n vmusr --blockFd 3

== EDIT ==

Corrected a typo in Rex Dieter's name.