You could use a
Teensy 4.0 for this. It has a second, USB Host -capable port on pads (D+ and D-) on the bottom side. Use
Teensyduino, the Teensy add-on to the Arduino environment, and the
USBHost_t36 library for USB Host support; it includes USB Serial support.
I recommend you keep the original USB micro connector for the power supply, so that you don't need to cut any traces on the Teensy (VUSB-VIN on the back side). This way, without cutting the trace, when connected to a host computer, the host will power the Teensy and the CH340 tester via USB; and when working standalone, you just connect an USB power bank to the Teensy USB connector.
There is a discussion forum dedicated for Teensy development at
https://forum.pjrc.com/.
The CH340 has had Linux drivers since 2007 or so; see
drivers/usb/serial/ch341.c.
These chips are way less scary to program/control than one might believe. First, see the
ch341_control_out() and
ch340_control_in() functions. (The
usb/core/message.c:usb_control_msg() function constructs and sends one USB control message to the device, but the
ch341_control_out() determines its contents. So, it is just a matter of sending and receiving USB control messages to configure the CH340 –– and you can look up the necessary message data from the above-linked drivers/usb/serial/ch341.c file from the Linux kernel –– to configure the chip.)
Add an EC11 or similar encoder with a button, maybe a small OLED display, wire up a socket for the adapter, add a capacitor for the 5V USB line provided to the CH340 chip, maybe some Schottky diodes and current limiting resistors in case the chip is placed the wrong way on the adapter, and the rest should be software, methinks.