Touchpad not working properly on a dell vostro laptop

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Distribution (run cat /etc/os-release):

NAME="Pop!_OS"
VERSION="22.04 LTS"
ID=pop
ID_LIKE="ubuntu debian"
PRETTY_NAME="Pop!_OS 22.04 LTS"
VERSION_ID="22.04"
HOME_URL="https://pop.system76.com"
SUPPORT_URL="https://support.system76.com"
BUG_REPORT_URL="https://github.com/pop-os/pop/issues"
PRIVACY_POLICY_URL="https://system76.com/privacy"
VERSION_CODENAME=jammy
UBUNTU_CODENAME=jammy
LOGO=distributor-logo-pop-os

Related Application and/or Package Version (run apt policy $PACKAGE NAME):
N/A

Issue/Bug Description:
Installed Pop!_OS on a Dell Vostro 14-3468, everything seems ok but the touchpad is not behaving properly.
I can move the cursor on screen using the touchpad easily and tap to click and double-finger-tap to right click works fine.

When pressing the bottom-left and bottom-right on the touchpad I can hear a button press sound but nothing happens on screen and hence I can't use the touchpad to drag and drop icons or resize windows.

Essentially the touchpad is working partially and the clicks at the bottom don't work.

Steps to reproduce :

• Get your hands on a Dell Vostro 14-3468
• Nuke windows and install Pop!_OS on it.
• Touchpad click on pressing the bottom stops working

Expected behavior:
Expecting the bottom left click to work so that I can hold it to resize windows or drag stuff.

Other Notes:

• Tried using xev, clicking the button does nothing.
• xinput output

⎡ Virtual core pointer                    	id=2	[master pointer  (3)]
⎜   ↳ Virtual core XTEST pointer              	id=4	[slave  pointer  (2)]
⎜   ↳ Synaptics TM3252-001                    	id=11	[slave  pointer  (2)]
⎣ Virtual core keyboard                   	id=3	[master keyboard (2)]
    ↳ Virtual core XTEST keyboard             	id=5	[slave  keyboard (3)]
    ↳ Video Bus                               	id=7	[slave  keyboard (3)]
    ↳ Sleep Button                            	id=9	[slave  keyboard (3)]
    ↳ Intel HID events                        	id=12	[slave  keyboard (3)]
    ↳ AT Translated Set 2 keyboard            	id=14	[slave  keyboard (3)]
    ↳ Power Button                            	id=8	[slave  keyboard (3)]
    ↳ Power Button                            	id=6	[slave  keyboard (3)]
    ↳ Integrated_Webcam_HD: Integrate         	id=10	[slave  keyboard (3)]
    ↳ Dell WMI hotkeys                        	id=13	[slave  keyboard (3)]

• I have tried changing gnome tweaks mouse emulation settings, it does not help.