Sound problem in Huawei laptop with Conexant CX8070 chip

My laptop is a Huawei MDZ-WXX9X, with the sound chip Conexant CX8070, and I'm running ubuntu 22.04.
I'm encountering the following two problems:

1. the sound is horrible in comparison to windows (I've dual-boot).
2. when I plug a Jack cable, the sound becomes normal, but the output comes both from the laptop's speaker and the headphones.

I've tried to assign the model of the card sound that I have to this options snd-hda-intel model=MODEL in the file /etc/modprobe.d/alsa-base.conf, like what they said here, but I didn't find Conexant CX8070 in /usr/share/doc/alsa-base/driver/HD-Audio-Models.txt.gz. I also tried to assign laptop, which is the basic laptop config (default), but I still have the same problem.

here is the output of sudo lspci -v:

00:1f.3 Multimedia audio controller: Intel Corporation Tiger Lake-LP Smart Sound Technology Audio Controller (rev 20)
    Subsystem: Device 1e83:3e35
    Flags: bus master, fast devsel, latency 32, IRQ 186, IOMMU group 12
    Memory at 601d1b0000 (64-bit, non-prefetchable) [size=16K]
    Memory at 601d000000 (64-bit, non-prefetchable) [size=1M]
    Capabilities: [50] Power Management version 3
    Capabilities: [80] Vendor Specific Information: Len=14 <?>
    Capabilities: [60] MSI: Enable+ Count=1/1 Maskable- 64bit+
    Kernel driver in use: sof-audio-pci-intel-tgl
    Kernel modules: snd_hda_intel, snd_sof_pci_intel_tgl

There are some workarounds listed here: https://github.com/thesofproject/linux/issues/3350 The general consensus seems to wait for a kernel patch