Touchpad not working on laptop Fujitsu E5511

[pigs-on-the-swim]

Description: Ubuntu 20.04.4 LTS
Release: 20.04

Touchpad ELAN or DesignWare (??) not working on laptop Fujitsu E5511
The built in touchpad does not work after start of Ubuntu.
current installation is new, first start, no updates yet, build in keyboard is working properly.

Workaround:
start terminal, manually invoke
sudo modprobe i2c-hid-acpi
makes touchpad work.

Expected behaviour:
Touchpad works without manual intervention.

Question:
Could you please investigate if a proper solution is possible or what to do?

Remark: login screen still works proper; this is NOT the case any more after very first reboot.
After very first reboot KEYBOARD and TOUCHPAD do not work any longer; login is not possible, no "mouse", no input by built in keyboard;

Remark (after first reboot):
Comparing the list of modules before/after invoking "sudo modprobe i2c-hid-acpi" I see this diff:

user@machine:~$ diff cat-proc-modules__withKeyBoard.txt cat-proc-modules__noKeyBoard.txt
1,6d0
< joydev 28672 0 - Live 0xffffffffc0be0000
< hid_multitouch 28672 0 - Live 0xffffffffc09af000
< hid_generic 16384 0 - Live 0xffffffffc0962000
< i2c_hid_acpi 16384 0 - Live 0xffffffffc06a9000
< i2c_hid 28672 1 i2c_hid_acpi, Live 0xffffffffc06bb000
< hid 139264 3 hid_multitouch,hid_generic,i2c_hid, Live 0xffffffffc098c000
160c154
< pinctrl_tigerlake 32768 1 - Live 0xffffffffc0022000
---
> pinctrl_tigerlake 32768 0 - Live 0xffffffffc0022000

I can not understand or interpret this.

REMARK:
after invoking "sudo modprobe i2c-hid-acpi" dmesg says:

[ 187.322961] hid: raw HID events driver (C) Jiri Kosina
[ 187.444671] input: 0X45 0X4C 0X41 0X4E 04F3:308C Mouse as /devices/pci0000:00/0000:00:15.3/i2c_designware.2/i2c-3/i2c-0X45 0X4C 0X41 0X4E 0X30 0X44 0X30 0X30 0X00:00/0018:04F3:308C.0001/input/input30
[ 187.444829] input: 0X45 0X4C 0X41 0X4E 04F3:308C Touchpad as /devices/pci0000:00/0000:00:15.3/i2c_designware.2/i2c-3/i2c-0X45 0X4C 0X41 0X4E 0X30 0X44 0X30 0X30 0X00:00/0018:04F3:308C.0001/input/input32
[ 187.444923] hid-generic 0018:04F3:308C.0001: input,hidraw0: I2C HID v1.00 Mouse [0X45 0X4C 0X41 0X4E 04F3:308C] on i2c-0X45 0X4C 0X41 0X4E 0X30 0X44 0X30 0X30 0X00:00
[ 187.574129] input: 0X45 0X4C 0X41 0X4E 04F3:308C Mouse as /devices/pci0000:00/0000:00:15.3/i2c_designware.2/i2c-3/i2c-0X45 0X4C 0X41 0X4E 0X30 0X44 0X30 0X30 0X00:00/0018:04F3:308C.0001/input/input33
[ 187.574268] input: 0X45 0X4C 0X41 0X4E 04F3:308C Touchpad as /devices/pci0000:00/0000:00:15.3/i2c_designware.2/i2c-3/i2c-0X45 0X4C 0X41 0X4E 0X30 0X44 0X30 0X30 0X00:00/0018:04F3:308C.0001/input/input35
[ 187.574358] hid-multitouch 0018:04F3:308C.0001: input,hidraw0: I2C HID v1.00 Mouse [0X45 0X4C 0X41 0X4E 04F3:308C] on i2c-0X45 0X4C 0X41 0X4E 0X30 0X44 0X30 0X30 0X00:00

(NO, I did NOT attach external devices like mouse or so)

REMARK:
(after invoking "sudo modprobe i2c-hid-acpi")
xinput tells me:

:~$ xinput
⎡ Virtual core pointer id=2 [master pointer (3)]
⎜ ↳ Virtual core XTEST pointer id=4 [slave pointer (2)]
⎜ ↳ 0X45 0X4C 0X41 0X4E 04F3:308C Mouse id=14 [slave pointer (2)]
⎜ ↳ 0X45 0X4C 0X41 0X4E 04F3:308C Touchpad id=15 [slave pointer (2)]
⎣ Virtual core keyboard id=3 [master keyboard (2)]
    ↳ Virtual core XTEST keyboard id=5 [slave keyboard (3)]
    ↳ Fujitsu FUJ02E3 id=6 [slave keyboard (3)]
    ↳ Video Bus id=7 [slave keyboard (3)]
    ↳ Power Button id=8 [slave keyboard (3)]
    ↳ FJ Camera: FJ Camera id=9 [slave keyboard (3)]
    ↳ FJ Camera: IR Camera id=10 [slave keyboard (3)]
    ↳ Intel HID events id=11 [slave keyboard (3)]
    ↳ Intel HID 5 button array id=12 [slave keyboard (3)]
    ↳ AT Translated Set 2 keyboard id=13 [slave keyboard (3)]

ProblemType: Bug
DistroRelease: Ubuntu 20.04
Package: linux-image-5.13.0-30-generic 5.13.0-30.33~20.04.1
ProcVersionSignature: Ubuntu 5.13.0-30.33~20.04.1-generic 5.13.19
Uname: Linux 5.13.0-30-generic x86_64
ApportVersion: 2.20.11-0ubuntu27.21
Architecture: amd64
CasperMD5CheckResult: skip
CurrentDesktop: ubuntu:GNOME
Date: Mon Apr 25 19:32:20 2022
InstallationDate: Installed on 2022-04-25 (0 days ago)
InstallationMedia: Ubuntu 20.04.4 LTS "Focal Fossa" - Release amd64 (20220223)
ProcEnviron:
 TERM=xterm-256color
 PATH=(custom, no user)
 XDG_RUNTIME_DIR=<set>
 LANG=de_DE.UTF-8
 SHELL=/bin/bash
SourcePackage: linux-signed-hwe-5.13
UpgradeStatus: No upgrade log present (probably fresh install)