I can change basically any section from Tweaks → Appearance → Themes properly, except for the Icons, which doesn't seem to be applied for most of the options.
Here's my Home folder using Yaru for icons:

Here's my Home folder using Humanity, Humanity-Dark, LoginIcons and a couple more. Same output for all of them.

When I try to use alternative themes, such as Dracula, Nordic, Arc-Darkest and Material-Black-Frost, the output is the same. It looks like some kind of system default. Adwaita (marked as default), DMZ-Black and DMZ-White, which are native on my OS, also look the same. This is how they look:

Here is some useful info:
My GNOME version is 3.38.5.
~: cat /usr/share/gnome/gnome-version.xml
<?xml version="1.0"?>
<gnome-version>
<platform>3</platform>
<minor>38</minor>
<micro>5</micro>
<distributor>Ubuntu</distributor>
<!--<date></date>-->
My GTK version is 3.24.25.
~: dpkg -l libgtk2.0-0 libgtk-3-0
Desired=Unknown/Install/Remove/Purge/Hold
| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend
|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)
||/ Name Version Architecture Description
+++-=================-==================-============-==================================================
ii libgtk-3-0:amd64 3.24.25-1ubuntu4.1 amd64 GTK graphical user interface library
ii libgtk2.0-0:amd64 2.24.33-1ubuntu2 amd64 GTK graphical user interface library - old version
The OS is Ubuntu 21.04.
I tried logging in, logging out and even restarting.
I got the non-native themes from Gnome-look.
Icons are stored in ~/.icons
and themes in ~/.themes
.
gnome-tweaks
version is 3.34.0.
I use 1920x1080 resolution, even though the native resolution from my hardware is 1366x768. The issue happens in both cases.
No message is provided when I change icons.