systemd-logind: loss of input devices when logging in after restart

# Steps to reproduce

1) Login as a regular user.
2) `sudo systemctl restart systemd-logind`

This boots you back to GDM, as you would expect.

3) Login as a user.
4) Wait a few seconds.

# Expected behaviour

I can continue to use my system normally.

# Actual behaviour

My keyboard and mouse stop working; unplugging/replugging has no effect. Everything on screen continues to behave normally.

# Debugging Notes

I noticed, when Ctrl-Alt-F'ing around trying to figure out what was going on, that there are _two_ GDM sessions apparently running after the logind restart.

Furthermore, I logged in on a console (Ctrl-Alt-F2) before performing the restart of logind, and when my keyboard stopped working in my graphical session, typing commands still worked! (I couldn't see this console, obviously, but I tested it by typing `mplayer Music/*/*` and observing music start playing.)

ProblemType: Bug
DistroRelease: Ubuntu 20.10
Package: systemd 246.6-1ubuntu1
ProcVersionSignature: Ubuntu 5.8.0-36.40-generic 5.8.18
Uname: Linux 5.8.0-36-generic x86_64
NonfreeKernelModules: zfs zunicode zavl icp zcommon znvpair nvidia_modeset nvidia
ApportVersion: 2.20.11-0ubuntu50.3
Architecture: amd64
CasperMD5CheckResult: skip
Date: Fri Jan 8 10:06:56 2021
InstallationDate: Installed on 2019-05-07 (611 days ago)
InstallationMedia: Ubuntu 18.04.2 LTS "Bionic Beaver" - Release amd64 (20190210)
MachineType: Gigabyte Technology Co., Ltd. B450M DS3H
ProcKernelCmdLine: BOOT_IMAGE=/vmlinuz-5.8.0-36-generic root=/dev/mapper/ubuntu--vg-root ro quiet splash resume=UUID=73909634-a75d-42c9-8f66-a69138690756 pcie_aspm=off vt.handoff=7
SourcePackage: systemd
SystemdDelta:
 [EXTENDED] /lib/systemd/system/rc-local.service → /lib/systemd/system/rc-local.service.d/debian.conf
 [EXTENDED] /lib/systemd/system/systemd-logind.service → /etc/systemd/system/systemd-logind.service.d/override.conf
 [EXTENDED] /lib/systemd/system/user@.service → /lib/systemd/system/user@.service.d/timeout.conf

 3 overridden configuration files found.
SystemdFailedUnits:
 Error: command ['systemctl', 'status', '--full', '●'] failed with exit code 4: Invalid unit name "●" escaped as "\xe2\x97\x8f" (maybe you should use systemd-escape?).
 Unit \xe2\x97\x8f.service could not be found.
 ------
 Error: command ['systemctl', 'status', '--full', '●'] failed with exit code 4: Invalid unit name "●" escaped as "\xe2\x97\x8f" (maybe you should use systemd-escape?).
 Unit \xe2\x97\x8f.service could not be found.
UpgradeStatus: Upgraded to groovy on 2020-06-22 (199 days ago)
dmi.bios.date: 01/25/2019
dmi.bios.release: 5.13
dmi.bios.vendor: American Megatrends Inc.
dmi.bios.version: F4
dmi.board.asset.tag: Default string
dmi.board.name: B450M DS3H-CF
dmi.board.vendor: Gigabyte Technology Co., Ltd.
dmi.board.version: x.x
dmi.chassis.asset.tag: Default string
dmi.chassis.type: 3
dmi.chassis.vendor: Default string
dmi.chassis.version: Default string
dmi.modalias: dmi:bvnAmericanMegatrendsInc.:bvrF4:bd01/25/2019:br5.13:svnGigabyteTechnologyCo.,Ltd.:pnB450MDS3H:pvrDefaultstring:rvnGigabyteTechnologyCo.,Ltd.:rnB450MDS3H-CF:rvrx.x:cvnDefaultstring:ct3:cvrDefaultstring:
dmi.product.family: Default string
dmi.product.name: B450M DS3H
dmi.product.sku: Default string
dmi.product.version: Default string
dmi.sys.vendor: Gigabyte Technology Co., Ltd.