Understandable, since this is a bit underdocumented. But there is a reason that: It is very simple.
There's sort of a manual here: https://adastra-soft.com/wp-content/uploads/2021/06/JDY-31_manual_2.pdf
The bluetooth module operates in two distinct modes: Transparent when connected to a Bluetooth peer, or AT command mode when Bluetooth is disconnected. So you have to configure it with a wired connection, using e.g a USB UART module.
Connect (GND, 3.3V, RX and TX crossed) the USB module to the Bluetooth module and configure minicom or whatever for 9600 8N1 using the appropriate ttyUSBx device.
Note that the AT interpreter is a bit weird. It doesn't like CR. Queries do not end in "?". New values follow the set command without any space or "=" separator between, even if the similar query result includes "=".
The most important commands are
AT+BAUD (value is a single digit: 4=9600, 5=19200, 6=38400, 7=57600, 8=115200, 9=128000)
AT+NAME
AT+LADDR
AT+RESET
AT+ENLOG (log connections: 0=off, 1=on)
AT+VERSION
To change the BAUD rate to 115200, you'd simply do (this will break the session until you match the USB baud rate of course)
AT+BAUD8
AT+RESET
That's really all you need.
But I like to change a couple of other settings for convenience. A unique name makes it much easier to discover the correct module if you have more than one. And I like to include the configured speed in the name so I don't have to guess or remember.
The modules also tend to all have the same mac address, so change it if you have more than one. Note that they also seem to match only on the last 3(?) bytes. So make those unique.
The modules are completely transparent when connected to a Bluetooth peer, but they will by default print CONNECTING>>CONNECTED to the UART when a connection is established. This usually doesn't matter to the console device. But it can be a problem if the bootloader accepts any key press as a stop signal and the message is printed at the wrong time. Chances of that are actually much higher than youd' think, since the Bluetooth module and console device share power supply. This syncronizes device boot with a Bluetooth connection if you have some console server trying to keep the session up. Luckily the message can be disabled with AT+ENLOG.
So a complete configuration could be like
AT+BAUD8
AT+NAMEmy-console-115k2
AT+LADDRBD6C0000BEEF
AT+ENLOG0
AT+RESET
It is also possible to reconfigure the module after installing it, as long as you have some other way in - like ssh. Just disconnect any Bluetooth peer and echo the AT commands to /dev/console. If you forgot to diable the log messages for example:
echo -ne "AT+ENLOG0\n" >/dev/console