Can't get 60Hz 4k on Dell XPS 13 9370 Ubuntu 22.04, only 30Hz works

I just got a Samsung LU28R550UQNXZA (28-inch 4K UHD) monitor, connected to a Dell XPS 13 9370 running Ubuntu 22.04.1 (X11). It works except that the highest supported refresh rate is 30Hz.

I'm using a USB-C to HDMI/USB-A adapter, but I'm pretty sure there's no issue with that or the cable because the same thing connected to a MacBook Pro gives 60Hz refresh rate.

What I tried without any success:

• It's the same with or without scaling (100% and 200%)
• Restart after connecting the monitor
• Tried all USB-C ports and different adapters (the same thing works with MacBook Pro)
• Tried manually adding the 60Hz using cvt and xrandr

My laptop spec:

• CPU: Intel® Core™ i7-8550U
• Graphics: Mesa Intel® UHD Graphics 620 (KBL GT2)

xrandr --verbose output (truncated):

...
DP-1 connected primary 3840x2160+0+0 (0x6c) normal (normal left inverted right x axis y axis) 632mm x 360mm
    Identifier: 0x42
    Timestamp:  16459755
    Subpixel:   unknown
    Gamma:      1.0:1.0:1.0
    Brightness: 1.0
    Clones:    
    CRTC:       0
    CRTCs:      1 0 2
    Transform:  1.000000 0.000000 0.000000
                0.000000 1.000000 0.000000
                0.000000 0.000000 1.000000
               filter: 
    EDID: 
        00ffffffffffff004c2d171055373930
        2c200103803f24782ac8b5ad50449e25
        0f5054bfef80714f810081c081809500
        a9c0b300010108e80030f2705a80b058
        8a0078682100001e000000fd00324b1e
        873c000a202020202020000000fc004c
        5532385235350a2020202020000000ff
        0048434a544230323239390a202001aa
        020335f04961120313041f10605f2309
        070783010000e305c0006b030c001000
        b83c2000200167d85dc401788003e20f
        81e3060501023a801871382d40582c45
        0078682100001e023a80d072382d4010
        2c458078682100001e04740030f2705a
        80b0588a0078682100001e565e00a0a0
        a029503020350078682100001a000059
    _MUTTER_PRESENTATION_OUTPUT: 0 
    HDCP Content Type: HDCP Type0 
        supported: HDCP Type0, HDCP Type1
    Content Protection: Undesired 
        supported: Undesired, Desired, Enabled
    Colorspace: Default 
        supported: Default, RGB_Wide_Gamut_Fixed_Point, RGB_Wide_Gamut_Floating_Point, opRGB, DCI-P3_RGB_D65, BT2020_RGB, BT601_YCC, BT709_YCC, XVYCC_601, XVYCC_709, SYCC_601, opYCC_601, BT2020_CYCC, BT2020_YCC
    max bpc: 12 
        range: (6, 12)
    Broadcast RGB: Automatic 
        supported: Automatic, Full, Limited 16:235
    audio: auto 
        supported: force-dvi, off, auto, on
    subconnector: HDMI 
        supported: Unknown, VGA, DVI-D, HDMI, DP, Wireless, Native
    link-status: Good 
        supported: Good, Bad
    CTM: -649236511 0 560760480 0 60196823 0 172408752 0 -136459090 0 28668150 -2147483648 40140107 0 45368128 -2147483648 
        18007942 1 
    CONNECTOR_ID: 103 
        supported: 103
    non-desktop: 0 
        range: (0, 1)
  3840x2160 (0x6c) 297.000MHz +HSync +VSync *current
        h: width  3840 start 4016 end 4104 total 4400 skew    0 clock  67.50KHz
        v: height 2160 start 2168 end 2178 total 2250           clock  30.00Hz
  3840x2160 (0x6d) 296.703MHz +HSync +VSync
        h: width  3840 start 4016 end 4104 total 4400 skew    0 clock  67.43KHz
        v: height 2160 start 2168 end 2178 total 2250           clock  29.97Hz
  2560x1440 (0x6e) 241.500MHz +HSync -VSync
        h: width  2560 start 2608 end 2640 total 2720 skew    0 clock  88.79KHz
        v: height 1440 start 1443 end 1448 total 1481           clock  59.95Hz
  1920x1080 (0x6f) 148.500MHz +HSync +VSync
        h: width  1920 start 2008 end 2052 total 2200 skew    0 clock  67.50KHz
        v: height 1080 start 1084 end 1089 total 1125           clock  60.00Hz
...

@matigo was right. Could get 60Hz refresh rate using USB-C to DisplayPort cable.