Wireless USB adapters used presently are Buffalo WI-U2-433DM that would have the rtl8812au specification, and Chinese EDUP with the rtl8811au.
The PC used is FMV-AH550/5B (core i5, memory 4Gbx2, SSD 500Gb). There is no option for a 'secure boot' in the BIOS. The OS is the Linux Mint Wilma Cinnamon ver.22.

I could not set up the wifi on the Q4OS and the Ubuntu 22.04LTS at all, which was unexpectedly troublesome. But as I got to understand more about the linux, I am able to set up the wifi.

Anyway in conclusion, it is found that if the rtl8821au is installed correctly in the linux mint, the rtl8811au and the rtl8812au work at dual bands (2.4/5GHz).

The procedure to install the drivers is as follows, referring to https://github.com/morrownr/8821au-20210708 [Note],*

$ sudo apt install git
$ git clone https://github.com/morrownr/8821au-20210708
$ cd 8821au-20210708
$ sudo sh install-driver.sh
then,
cntl+x and
Y ---> rebooting

After rebooting, either of the USB adapters is plugged in, then the 5GHz band is selected, hence the connection speed is about 300Mbps (upload: 220Mbps).

Note:
*Another version is in
https://github.com/morrownr/8812au-20210820, which can also be used to activate the wifi.