Counter Strike 2 doesn't start with the error "Failed to initialize Vulkan"

I can't launch Counter Strike 2 on my Dell laptop, with Intel Haswell-ULT graphics, running Linux Mint. When I try I get an error telling me to check if my GPU supports Vulkan 1.2+:

System:
  Kernel: 5.15.0-113-generic x86_64 bits: 64 compiler: gcc v: 11.4.0 Desktop: MATE 1.26.0
    info: mate-panel wm: marco 1.26.0 dm: LightDM 1.30.0 Distro: Linux Mint 21.3 Virginia
    base: Ubuntu 22.04 jammy
Machine:
  Type: Laptop System: Dell product: Latitude E7440 v: 00 serial:  Chassis:
    type: 9 serial: 
  Mobo: Dell model: 091TRH v: A00 serial:  UEFI: Dell v: A28
    date: 06/13/2019
CPU:
  Info: dual core model: Intel Core i5-4300U bits: 64 type: MT MCP smt: enabled arch: Haswell
    rev: 1 cache: L1: 128 KiB L2: 512 KiB L3: 3 MiB
  Speed (MHz): avg: 2694 high: 2852 min/max: 800/2900 cores: 1: 2736 2: 2594 3: 2852 4: 2595
    bogomips: 19953
  Flags: avx avx2 ht lm nx pae sse sse2 sse3 sse4_1 sse4_2 ssse3 vmx
Graphics:
  Device-1: Intel Haswell-ULT Integrated Graphics vendor: Dell driver: i915 v: kernel ports:
    active: eDP-1 empty: DP-1,HDMI-A-1,HDMI-A-2 bus-ID: 00:02.0 chip-ID: 8086:0a16 class-ID: 0300
  Device-2: Microdia Integrated Webcam type: USB driver: uvcvideo bus-ID: 2-4:2
    chip-ID: 0c45:64d2 class-ID: 0e02
  Display: x11 server: X.Org v: 1.21.1.4 compositor: marco v: 1.26.0 driver: X:
    loaded: modesetting unloaded: fbdev,vesa gpu: i915 display-ID: :0 screens: 1
  Screen-1: 0 s-res: 1366x768 s-dpi: 96 s-size: 361x203mm (14.2x8.0") s-diag: 414mm (16.3")
  Monitor-1: eDP-1 model: Chi Mei Innolux res: 1366x768 hz: 60 dpi: 112
    size: 309x174mm (12.2x6.9") diag: 355mm (14") modes: 1366x768
  OpenGL: renderer: Mesa Intel HD Graphics 4400 (HSW GT2)
    v: 4.6 Mesa 24.2~git2407100600.ae3e0a~oibaf~j (git-ae3e0ae 2024-07-10 jammy-oibaf-ppa)
    compat-v: 4.6 direct render: Yes
Audio:
  Device-1: Intel Haswell-ULT HD Audio vendor: Dell driver: snd_hda_intel v: kernel
    bus-ID: 00:03.0 chip-ID: 8086:0a0c class-ID: 0403
  Device-2: Intel 8 Series HD Audio vendor: Dell driver: snd_hda_intel v: kernel bus-ID: 00:1b.0
    chip-ID: 8086:9c20 class-ID: 0403
  Sound Server-1: ALSA v: k5.15.0-113-generic running: yes
  Sound Server-2: PulseAudio v: 15.99.1 running: yes
  Sound Server-3: PipeWire v: 0.3.48 running: yes
Network:
  Device-1: Intel Ethernet I218-LM vendor: Dell driver: e1000e v: kernel port: f080
    bus-ID: 00:19.0 chip-ID: 8086:155a class-ID: 0200
  IF: eno1 state: up speed: 100 Mbps duplex: full mac: 
  Device-2: Intel Wireless 7260 driver: iwlwifi v: kernel pcie: speed: 2.5 GT/s lanes: 1
    bus-ID: 02:00.0 chip-ID: 8086:08b1 class-ID: 0280
  IF: wlp2s0 state: down mac: 
RAID:
  Hardware-1: Intel 82801 Mobile SATA Controller [RAID mode] driver: ahci v: 3.0 port: f060
    bus-ID: 00:1f.2 chip-ID: 8086:282a rev: N/A class-ID: 0104
Drives:
  Local Storage: total: 465.76 GiB used: 152.01 GiB (32.6%)
  ID-1: /dev/sda vendor: Western Digital model: WD5000LPVX-75V0TT0 size: 465.76 GiB
    speed: 6.0 Gb/s type: HDD rpm: 5400 serial:  rev: 1A01 scheme: GPT
Partition:
  ID-1: / size: 456.89 GiB used: 152 GiB (33.3%) fs: ext4 dev: /dev/sda2
  ID-2: /boot/efi size: 511 MiB used: 11.9 MiB (2.3%) fs: vfat dev: /dev/sda1
Swap:
  ID-1: swap-1 type: file size: 2 GiB used: 235.2 MiB (11.5%) priority: -2 file: /swapfile
USB:
  Hub-1: 1-0:1 info: Full speed or root hub ports: 2 rev: 2.0 speed: 480 Mb/s chip-ID: 1d6b:0002
    class-ID: 0900
  Hub-2: 1-1:2 info: Intel Integrated Rate Matching Hub ports: 8 rev: 2.0 speed: 480 Mb/s
    chip-ID: 8087:8000 class-ID: 0900
  Hub-3: 2-0:1 info: Hi-speed hub with single TT ports: 9 rev: 2.0 speed: 480 Mb/s
    chip-ID: 1d6b:0002 class-ID: 0900
  Device-1: 2-2:3 info: USB Optical Mouse type: Mouse driver: hid-generic,usbhid interfaces: 1
    rev: 1.1 speed: 1.5 Mb/s power: 100mA chip-ID: 30fa:0300 class-ID: 0301
  Device-2: 2-4:2 info: Microdia Integrated Webcam type: Video driver: uvcvideo interfaces: 2
    rev: 2.0 speed: 480 Mb/s power: 500mA chip-ID: 0c45:64d2 class-ID: 0e02
  Hub-4: 3-0:1 info: Super-speed hub ports: 4 rev: 3.0 speed: 5 Gb/s chip-ID: 1d6b:0003
    class-ID: 0900
Sensors:
  System Temperatures: cpu: 58.0 C mobo: 44.0 C sodimm: SODIMM C
  Fan Speeds (RPM): cpu: 4709
Repos:
  Packages: 2402 apt: 2393 flatpak: 9
  No active apt repos in: /etc/apt/sources.list
  Active apt repos in: /etc/apt/sources.list.d/microsoft-edge.list
    1: deb [arch=amd64] https: //packages.microsoft.com/repos/edge/ stable main
  Active apt repos in: /etc/apt/sources.list.d/official-package-repositories.list
    1: deb https: //mirror.albony.xyz/linuxmint virginia main upstream import backport
    2: deb http: //archive.ubuntu.com/ubuntu jammy main restricted universe multiverse
    3: deb http: //archive.ubuntu.com/ubuntu jammy-updates main restricted universe multiverse
    4: deb http: //archive.ubuntu.com/ubuntu jammy-backports main restricted universe multiverse
    5: deb http: //security.ubuntu.com/ubuntu/ jammy-security main restricted universe multiverse
  Active apt repos in: /etc/apt/sources.list.d/oibaf-graphics-drivers-jammy.list
    1: deb [signed-by=/etc/apt/keyrings/oibaf-graphics-drivers-jammy.gpg] https: //ppa.launchpadcontent.net/oibaf/graphics-drivers/ubuntu jammy main
  Active apt repos in: /etc/apt/sources.list.d/steam.list
    1: deb [arch=amd64 signed-by=/usr/share/keyrings/steam.gpg] http: //repo.steampowered.com/steam/ stable steam
  Active apt repos in: /etc/apt/sources.list.d/vivaldi.list
    1: deb [arch=amd64] https: //repo.vivaldi.com/stable/deb/ stable main
  Active apt repos in: /etc/apt/sources.list.d/winehq-focal.sources
    1: deb [arch=amd64 i386] https: //dl.winehq.org/wine-builds/ubuntu focal main
Info:
  Processes: 222 Uptime: 3h 9m wakeups: 1 Memory: 7.66 GiB used: 2.29 GiB (29.9%) Init: systemd
  v: 249 runlevel: 5 Compilers: gcc: 11.4.0 alt: 11/12 Client: Unknown python3.10 client
  inxi: 3.3.13

Result from vulcaninfo:

-shellsession
$ vulcaninfo | grep "Vulkan Instance Version" 

WARNING: [Loader Message] Code 0 : terminator_CreateInstance: Failed to CreateInstance in ICD 2. 

Skipping ICD. WARNING: [Loader Message] Code 0 : terminator_CreateInstance:

 Failed to CreateInstance in ICD 4. Skipping ICD. 

MESA-INTEL: warning: Haswell Vulkan support is incomplete

 Vulkan Instance Version: 1.3.20