Using the standard desktop environment, with or without Wayland, the performance is terrible when using two monitors. Interestingly, watching 4k@24hz video on the second monitor is no problem at all, but GNOME is really laggy. But simple things like scrolling in a GTK window, or moving it, lags intolerably. It works fine on Windows.

I'm not sure what information would be useful to troubleshoot this, so please just ask. I'm on Mesa 22, but the older versions I tested were not better. Here's a bit of glxinfo.

    Vendor: Intel (0x8086)

    Device: Mesa Intel(R) Xe Graphics (TGL GT2) (0x9a49)

    Version: 22.0.0

    Accelerated: yes

    Video memory: 3072MB

    Unified memory: yes

    Preferred profile: core (0x1)

    Max core profile version: 4.6

    Max compat profile version: 4.6

    Max GLES1 profile version: 1.1

    Max GLES[23] profile version: 3.2

This is my 20-intel.conf:

Section "Device"

    Identifier "Intel Graphics"

    Driver "i915"

    Option "TearFree"    "true"

EndSection

I added this to make mpv play tear free videos. (This is also why I upgraded Mesa, and run Wayland.) Removing it has no impact on the desktop performance.

Some other info:

System:

  Kernel: 5.11.0-46-generic x86_64 

  bits: 64

  Desktop: Gnome 3.36.9 Distro: Ubuntu 20.04.3 LTS (Focal Fossa) 

Machine:

  Type: Laptop System: LENOVO product: 20VD v: ThinkBook 14 G2 ITL 

  Mobo: LENOVO model: LNVNB161216 v: SDK0J40697 WIN 

  UEFI: LENOVO v: F8CN34WW(V1.12) 

  date: 02/01/2021 

CPU:

  Topology: Quad Core model: 11th Gen Intel Core i7-1165G7 bits: 64 

  type: MT MCP L2 cache: 12.0 MiB 

  Speed: 1450 MHz min/max: 400/4700 MHz Core speeds (MHz): 1: 3504 2: 3388 

  3: 4100 4: 3698 5: 3835 6: 4023 7: 3916 8: 3347 

Graphics:

  Device-1: Intel driver: i915 v: kernel 

  Display: wayland server: X.Org 1.20.13 driver: i915 

  resolution: 1920x1080~24Hz, 1920x1080~60Hz 

  OpenGL: renderer: Mesa Intel Xe Graphics (TGL GT2) 

  v: 4.6 Mesa 22.0.0-devel (git-b5b105d 2022-01-21 focal-oibaf-ppa) 

Edit:
There are versions of this ThinkBook that also includes an Nvidia adapter, but I have one that only comes with Intel. Per lspci:

0000:00:02.0 VGA compatible controller: Intel Corporation Device 9a49 (rev 01)