I have forgotten the Messages from root Shell with journalctl -f | less. Sorry.

root@kali-linux:/home/cohst# journalctl -f | less
-- Logs begin at Mon 2019-11-25 20:14:11 CET. --
Nov 25 20:17:46 kali-linux rtkit-daemon[451]: Supervising 2 threads of 1 processes of 2 users.
Nov 25 20:17:46 kali-linux systemd[1127]: Started D-Bus User Message Bus.
Nov 25 20:17:46 kali-linux pulseaudio[1140]: E: [pulseaudio] bluez5-util.c: GetManagedObjects() failed: org.freedesktop.DBus.Error.AccessDenied: Rejected send message, 2 matched rules; type="method_call", sender=":1.187" (uid=1000 pid=1140 comm="/usr/bin/pulseaudio --daemonize=no ") interface="org.freedesktop.DBus.ObjectManager" member="GetManagedObjects" error name="(unset)" requested_reply="0" destination="org.bluez" (bus)
Nov 25 20:17:46 kali-linux systemd[1127]: Started Sound Service.
Nov 25 20:17:46 kali-linux systemd[1127]: Reached target Main User Target.
Nov 25 20:17:46 kali-linux systemd[1127]: Startup finished in 2.851s.
Nov 25 20:18:10 kali-linux sudo[1160]: pam_unix(sudo:auth): Couldn't open /etc/securetty: No such file or directory
Nov 25 20:18:18 kali-linux sudo[1160]: pam_unix(sudo:auth): Couldn't open /etc/securetty: No such file or directory
Nov 25 20:18:18 kali-linux sudo[1160]: cohst : TTY=pts/0 ; PWD=/home/cohst ; USER=root ; COMMAND=/bin/bash
Nov 25 20:18:18 kali-linux sudo[1160]: pam_unix(sudo:session): session opened for user root by cohst(uid=0)
Nov 25 20:18:41 kali-linux gdm-password][1172]: pam_unix(gdm-password:auth): Couldn't open /etc/securetty: No such file or directory
Nov 25 20:18:50 kali-linux gdm-password][1172]: pam_unix(gdm-password:auth): Couldn't open /etc/securetty: No such file or directory
Nov 25 20:18:50 kali-linux gdm-password][1172]: gkr-pam: unable to locate daemon control file
Nov 25 20:18:50 kali-linux gdm-password][1172]: pam_unix(gdm-password:session): session opened for user cohst by (uid=0)
Nov 25 20:18:50 kali-linux systemd-logind[505]: New session 6 of user cohst.
Nov 25 20:18:50 kali-linux systemd[1]: Started Session 6 of user cohst.
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: () Option "fd" "20"
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) event1 - Power Button: device removed
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: () Option "fd" "23"
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) event0 - AT Translated Set 2 keyboard: device removed
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: () Option "fd" "24"
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) event3 - VirtualPS/2 VMware VMMouse: device removed
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: () Option "fd" "25"
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) event2 - VirtualPS/2 VMware VMMouse: device removed
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) systemd-logind: got pause for 13:67
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) systemd-logind: got pause for 226:0
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) systemd-logind: got pause for 13:64
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) systemd-logind: got pause for 13:65
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[769]: (II) systemd-logind: got pause for 13:66
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[1186]: _XSERVTransSocketUNIXCreateListener: ...SocketCreateListener() failed
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[1186]: _XSERVTransMakeAllCOTSServerListeners: server already running
Nov 25 20:18:51 kali-linux /usr/lib/gdm3/gdm-x-session[1186]: (--) Log file renamed from "/home/cohst/.local/share/xorg/Xorg.pid-1188.log" to "/home/cohst/.local/share/xorg/Xorg.1.log"
Nov 25 20:18:52 kali-linux /usr/lib/gdm3/gdm-x-session[1186]: X.Org X Server 1.20.4
Nov 25 20:18:52 kali-linux /usr/lib/gdm3/gdm-x-session[1186]: X Protocol Version 11, Revision 0
Nov 25 20:18:52 kali-linux /usr/lib/gdm3/gdm-x-session[1186]: Build Operating System: Linux 4.9.0-8-amd64 i686 Debian
Nov 25 20:18:52 kali-linux /usr/lib/gdm3/gdm-x-session[1186]: Current Operating System: Linux kali-linux 5.3.0-kali2-686-pae 0000001 SMP Debian 5.3.9-3kali1 (2019-11-20) i686
Nov 25 20:18:52 kali-linux /usr/lib/gdm3/gdm-x-session[1186]: Kernel command line: BOOT_IMAGE=/boot/vmlinuz-5.3.0-kali2-686-p:

By now it works again, after a new start of the Hypervisor. Can you Image, that it has might something to do with VMware upgrade vmsa-2019-0020? I did not patch the Hypervisor up to now, but in the update of yesterday there were microcode updates for Kali Linux. I'm not sure if that has to something with that.

Ticket can be closed, I have installed the new Version of Kali 2020.1, the problem is solved.

Thanks, I closed the ticket.