Here is the screenshot on Ubuntu 22.04 LTS. Vulkan shows as disabled.

Now, the screenshot of Fedora where vulkan shows as enabled:

So, how do I enable vulkan on Ubuntu?
Edit 1:
Output of sudo lspci
:
00:00.0 Host bridge: Intel Corporation Ice Lake-LP Processor Host Bridge/DRAM Registers (rev 03)
00:02.0 VGA compatible controller: Intel Corporation Iris Plus Graphics G1 (Ice Lake) (rev 07)
00:04.0 Signal processing controller: Intel Corporation Device 8a03 (rev 03)
00:0d.0 USB controller: Intel Corporation Ice Lake Thunderbolt 3 USB Controller (rev 03)
00:12.0 Serial controller: Intel Corporation Ice Lake-LP Integrated Sensor Solution (rev 30)
00:14.0 USB controller: Intel Corporation Ice Lake-LP USB 3.1 xHCI Host Controller (rev 30)
00:14.2 RAM memory: Intel Corporation Ice Lake-LP DRAM Controller (rev 30)
00:15.0 Serial bus controller: Intel Corporation Ice Lake-LP Serial IO I2C Controller #0 (rev 30)
00:15.1 Serial bus controller: Intel Corporation Ice Lake-LP Serial IO I2C Controller #1 (rev 30)
00:16.0 Communication controller: Intel Corporation Ice Lake-LP Management Engine (rev 30)
00:1c.0 PCI bridge: Intel Corporation Ice Lake-LP PCI Express Root Port #5 (rev 30)
00:1c.6 PCI bridge: Intel Corporation Device 34be (rev 30)
00:1c.7 PCI bridge: Intel Corporation Device 34bf (rev 30)
00:1d.0 PCI bridge: Intel Corporation Device 34b4 (rev 30)
00:1f.0 ISA bridge: Intel Corporation Ice Lake-LP LPC Controller (rev 30)
00:1f.3 Audio device: Intel Corporation Ice Lake-LP Smart Sound Technology Audio Controller (rev 30)
00:1f.4 SMBus: Intel Corporation Ice Lake-LP SMBus Controller (rev 30)
00:1f.5 Serial bus controller: Intel Corporation Ice Lake-LP SPI Controller (rev 30)
01:00.0 3D controller: NVIDIA Corporation GP108M [GeForce MX330] (rev a1)
02:00.0 Network controller: Qualcomm Atheros QCA6174 802.11ac Wireless Network Adapter (rev 32)
03:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 15)
04:00.0 Non-Volatile memory controller: SK hynix BC511
Output of sudo find /sys | grep drivers.*00:02.0
:
/sys/bus/pci/drivers/ath10k_pci/0000:02:00.0
/sys/bus/pci/drivers/i915/0000:00:02.0
Edit 2:
Output of vulkaninfo
Also, I tried to go to chrome://flags/#enable-vulkan
and set it to enabled but that just made chrome stop working completely.