Dell inspiron 15 7000 touchpad buttons not working

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10

That does show it using libinput.

If you want to try and force synaptics then maybe you can use a conf file … heres mine:
/etc/X11/xorg.conf.d/71-synaptics.conf 

Section "InputClass"
    Identifier "touchpad catchall"
    Driver "synaptics"
    MatchIsTouchpad "on"
    MatchDevicePath "/dev/input/event*"
        Option "TapButton1" "1"
        Option "TapButton2" "3"
        Option "TapButton3" "2"
        Option "VertTwoFingerScroll" "on"
        Option "HorizTwoFingerScroll" "on"
#        Option "VertEdgeScroll" "off"
#        Option "HorizEdgeScroll" "off"
#        Option "CircularScrolling" "off"
#        Option "CircScrollTrigger" "2"
#        Option "EmulateTwoFingerMinZ" "40"
#        Option "EmulateTwoFingerMinW" "8"
#        Option "CoastingSpeed" "0"
#        Option "FingerLow" "30"
#        Option "FingerHigh" "50"
#        Option "MaxTapTime" "125"
EndSection

Section "InputClass"
        Identifier "touchpad ignore duplicates"
        MatchIsTouchpad "on"
        MatchOS "Linux"
        MatchDevicePath "/dev/input/mouse*"
        Option "Ignore" "on"
EndSection

(obviously the commented out options have no effect … they are left for convenience for you to tweak)