Test done under Trisquel 11 with kernels:

5.15.0-67-generic and 6.6.11-gnu

• Card reader: works
• Audio: works
• Jack audio: works
• Integrated Microphone: Works
• Jack Microphone: None
• USB2: works
• Ethernet RJ-45: None
• CD/DVD Reader: None
• FN keys: works
• HDMI: works
• HDMI audio: works
• Screen Luminosity control: works
• Sleep mode: Works
• Hibernate mode: not tested
• Webcam: Works (tested with cheese)
• Batterie : Works

The initial wireless intel card didn't work due to it's proprietary nature so I did a test by swapping it with a "Qualcomm Atheros QCA9565 / AR9565 Wireless Network Adapter [168c:0036]" and it worked perfectly.

lspci -nnk

00:00.0 Host bridge [0600]: Intel Corporation Device [8086:9b71] (rev 0c)
	Subsystem: ASUSTeK Computer Inc. Device [1043:1d11]
	Kernel driver in use: skl_uncore
00:02.0 VGA compatible controller [0300]: Intel Corporation CometLake-U GT2 [UHD Graphics] [8086:9b41] (rev 02)
	DeviceName: VGA
	Subsystem: ASUSTeK Computer Inc. CometLake-U GT2 [UHD Graphics] [1043:1d11]
	Kernel driver in use: i915
	Kernel modules: i915
00:04.0 Signal processing controller [1180]: Intel Corporation Xeon E3-1200 v5/E3-1500 v5/6th Gen Core Processor Thermal Subsystem [8086:1903] (rev 0c)
	Subsystem: ASUSTeK Computer Inc. Xeon E3-1200 v5/E3-1500 v5/6th Gen Core Processor Thermal Subsystem [1043:1d11]
	Kernel driver in use: proc_thermal
	Kernel modules: processor_thermal_device_pci_legacy
00:08.0 System peripheral [0880]: Intel Corporation Xeon E3-1200 v5/v6 / E3-1500 v5 / 6th/7th/8th Gen Core Processor Gaussian Mixture Model [8086:1911]
	Subsystem: ASUSTeK Computer Inc. Xeon E3-1200 v5/v6 / E3-1500 v5 / 6th/7th/8th Gen Core Processor Gaussian Mixture Model [1043:1d11]
00:12.0 Signal processing controller [1180]: Intel Corporation Comet Lake Thermal Subsytem [8086:02f9]
	Subsystem: ASUSTeK Computer Inc. Comet Lake Thermal Subsytem [1043:1d11]
	Kernel driver in use: intel_pch_thermal
	Kernel modules: intel_pch_thermal
00:14.0 USB controller [0c03]: Intel Corporation Comet Lake PCH-LP USB 3.1 xHCI Host Controller [8086:02ed]
	Subsystem: ASUSTeK Computer Inc. Comet Lake PCH-LP USB 3.1 xHCI Host Controller [1043:201f]
	Kernel driver in use: xhci_hcd
	Kernel modules: xhci_pci
00:14.2 RAM memory [0500]: Intel Corporation Comet Lake PCH-LP Shared SRAM [8086:02ef]
	Subsystem: Intel Corporation Comet Lake PCH-LP Shared SRAM [8086:7270]
00:14.3 Network controller [0280]: Intel Corporation Comet Lake PCH-LP CNVi WiFi [8086:02f0]
	DeviceName: WLAN
	Subsystem: Intel Corporation Comet Lake PCH-LP CNVi WiFi [8086:02a4]
	Kernel modules: iwlwifi
00:14.5 SD Host controller [0805]: Intel Corporation Comet Lake PCH-LP SCS3 [8086:02f5]
	Subsystem: Intel Corporation Comet Lake PCH-LP SCS3 [8086:7270]
	Kernel driver in use: sdhci-pci
	Kernel modules: sdhci_pci
00:15.0 Serial bus controller [0c80]: Intel Corporation Serial IO I2C Host Controller [8086:02e8]
	Subsystem: ASUSTeK Computer Inc. Serial IO I2C Host Controller [1043:1d11]
	Kernel driver in use: intel-lpss
	Kernel modules: intel_lpss_pci
00:15.1 Serial bus controller [0c80]: Intel Corporation Comet Lake Serial IO I2C Host Controller [8086:02e9]
	Subsystem: ASUSTeK Computer Inc. Comet Lake Serial IO I2C Host Controller [1043:1d11]
	Kernel driver in use: intel-lpss
	Kernel modules: intel_lpss_pci
00:16.0 Communication controller [0780]: Intel Corporation Comet Lake Management Engine Interface [8086:02e0]
	Subsystem: ASUSTeK Computer Inc. Comet Lake Management Engine Interface [1043:1d11]
	Kernel driver in use: mei_me
	Kernel modules: mei_me
00:17.0 SATA controller [0106]: Intel Corporation Comet Lake SATA AHCI Controller [8086:02d3]
	Subsystem: ASUSTeK Computer Inc. Comet Lake SATA AHCI Controller [1043:1d11]
	Kernel driver in use: ahci
	Kernel modules: ahci
00:1e.0 Communication controller [0780]: Intel Corporation Device [8086:02a8]
	Subsystem: ASUSTeK Computer Inc. Device [1043:1d11]
	Kernel driver in use: intel-lpss
	Kernel modules: intel_lpss_pci
00:1e.2 Serial bus controller [0c80]: Intel Corporation Device [8086:02aa]
	Subsystem: ASUSTeK Computer Inc. Device [1043:1d11]
	Kernel driver in use: intel-lpss
	Kernel modules: intel_lpss_pci
00:1f.0 ISA bridge [0601]: Intel Corporation Comet Lake PCH-LP LPC Premium Controller/eSPI Controller [8086:0284]
	Subsystem: ASUSTeK Computer Inc. Comet Lake PCH-LP LPC Premium Controller/eSPI Controller [1043:1d11]
00:1f.3 Audio device [0403]: Intel Corporation Comet Lake PCH-LP cAVS [8086:02c8]
	Subsystem: ASUSTeK Computer Inc. Comet Lake PCH-LP cAVS [1043:19ae]
	Kernel driver in use: snd_hda_intel
	Kernel modules: snd_hda_intel, snd_sof_pci_intel_cnl
00:1f.4 SMBus [0c05]: Intel Corporation Comet Lake PCH-LP SMBus Host Controller [8086:02a3]
	Subsystem: ASUSTeK Computer Inc. Comet Lake PCH-LP SMBus Host Controller [1043:1d11]
	Kernel driver in use: i801_smbus
	Kernel modules: i2c_i801
00:1f.5 Serial bus controller [0c80]: Intel Corporation Comet Lake SPI (flash) Controller [8086:02a4]
	Subsystem: Intel Corporation Comet Lake SPI (flash) Controller [8086:7270]
	Kernel driver in use: intel-spi
	Kernel modules: spi_intel_pci

lsusb

Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 001 Device 004: ID 13d3:56dd IMC Networks USB2.0 HD UVC WebCam
Bus 001 Device 003: ID 1516:7305 CompUSA SK7305 
Bus 001 Device 005: ID 8087:0aaa Intel Corp. Bluetooth 9460/9560 Jefferson Peak (JfP)
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub