You can try accessing the root shell through SSH, if you can, and check the files in the /etc/opkg/ folder to see where this build downloads additional packages from.
If the URL points to a manufacturer's website or downloads area, then it is possible that the packages there are custom-made, and do not contain the default LuCI web interface. But if they point to the 'downloads.openwrt.org' site, then you might be able to install the default OpenWRT LuCI web interface. You might also need some additional tuning to fix the web server's configuration so it loads the default LuCI correctly.
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If you want to get more involved in the process, and if I read the bootlog correctly, then the router has 64MB of RAM and 8MB of flash memory. The SoC is AR9330. A short Google search reveals the following page from OpenWRT Wiki: https://wiki.openwrt.org/toh/tp-link/tl-wr740n
The TP-Link TL-WR740N's hardware and bootlog seem to be very close to your router's, the primary differences seem to be in RAM size and the flash memory size. Based on these, you could consider fetching the OpenWRT buildroot environment for yourself, and building a minimal ramdisk-variant for the TL-WR740N. Then attempt to run this ramdisk version directly from memory by accessing the bootloader through a serial console, and using tftpboot and bootm commands to upload and run the ramdisk version.
Try out different things with the ramdisk variant, and see how it works. You can always safely return to the original firmware by powering off the router, and powering it back on again. If the ramdisk variant seems to work nicely, then it should be a simple process to create a copy of the device profile, and adjust the flash region ranges of the new device profile to match those in the current firmware so that things align correctly.
Do not, under any circumstances, flash the TL-WR740N's firmware onto the device. The bootlogs show that this firmware uses different region ranges for the flash memory, and these differences may cause the flash process to overwrite crucial data such as the bootloader or the ART region.