After struggling for a month, I found the solution just a few minutes after creating this post.
Sorry, I was just dumb… fixed via:
$ sudo rfkill
ID TYPE DEVICE SOFT HARD
0 bluetooth hci0 blocked unblocked
1 wlan phy0 blocked unblocked
$ sudo rfkill unblock wlan
$ sudo rfkill
ID TYPE DEVICE SOFT HARD
0 bluetooth hci0 blocked unblocked
1 wlan phy0 unblocked unblocked
$ iwctl station list
Devices in Station Mode
--------------------------------------------------------------------------------
Name State Scanning
--------------------------------------------------------------------------------
wlan0 connected
journal:
sudo[7292]: someone : TTY=pts/9 ; PWD=/home/someone ; USER=root ; COMMAND=/usr/sbin/rfkill unblock wlan
rfkill[7293]: unblock set for type wlan
kernel: iwlwifi 0000:aa:00.0: WRT: Failed to set DRAM buffer for alloc id 1, ret=-1
kernel: iwlwifi 0000:aa:00.0: WRT: Failed to set DRAM buffer for alloc id 2, ret=-1
kernel: iwlwifi 0000:aa:00.0: WRT: Failed to set DRAM buffer for alloc id 3, ret=-1
systemd[1]: Starting Load/Save RF Kill Switch Status...
systemd[1]: Started Load/Save RF Kill Switch Status.
systemd-networkd[483]: wlan0: Link UP
systemd[1]: systemd-rfkill.service: Succeeded.
systemd-networkd[483]: wlan0: Link DOWN
kernel: iwlwifi 0000:aa:00.0: WRT: Failed to set DRAM buffer for alloc id 1, ret=-1
kernel: iwlwifi 0000:aa:00.0: WRT: Failed to set DRAM buffer for alloc id 2, ret=-1
kernel: iwlwifi 0000:aa:00.0: WRT: Failed to set DRAM buffer for alloc id 3, ret=-1
systemd-networkd[483]: wlan0: Link UP
kernel: wlan0: authenticate with **:**:**:**:**:**
kernel: wlan0: send auth to **:**:**:**:**:** (try 1/3)
kernel: wlan0: authenticated
kernel: wlan0: associate with **:**:**:**:**:** (try 1/3)
kernel: wlan0: RX AssocResp from **:**:**:**:**:** (capab=0x11 status=0 aid=2)
kernel: wlan0: associated
kernel: wlan0: Limiting TX power to 23 (23 - 0) dBm as advertised by **:**:**:**:**:**
systemd-networkd[483]: wlan0: Gained carrier
systemd-networkd[483]: wlan0: Connected WiFi access point: SORRY (**:**:**:**:**:**)
iwd[671]: WARNING: src/resolve.c:resolve_systemd_set_dns() condition !systemd_state.is_ready failed
iwd[671]: WARNING: src/resolve.c:resolve_systemd_set_domains() condition !systemd_state.is_ready failed
Apparently, the mentioned error iwlwifi 0000:aa:00.0: firmware: failed to load iwlwifi-ty-a0-gf-a0-67.ucode (-2) is irrelevant.
I hope this post will be useful for others making the same mistake.