The current firmware version is 0.9.9 (latest version can be found on the website).
You can check the firmware version on your ESP-01 on the admin webpage found at https://tcp2elegoo.local/ (kit default) https://yourelegoo.local/ (yourelegoo is the name you gave your ESP-01, if you changed it) or https://ip-address/ (given by your router, e.g. 192.168.1.33).
You can update the firmware directly from the admin webpage or if required download the latest version at https://elegoo.wwfirst.ca/esp-01/Tcp2Serial-loader.bin. Browse to your Elegoo ESP-01 at https://yourelegoo/update to update the firmware with the downloaded Tcp2Serial-loader.bin file.