What firmware do the BL5340/BL5340PA modules ship with initially? Can they initially be programmed via UART or FOTA or is it necessary to implement the SWD Interface?

As per section 3.7 of the BL5340/BL5340PA datasheets (links provided below) , these modules ship with no firmware loaded. Therefore, there is no Bootloader loaded to enable loading applications via UART and no support for FOTA (Firmware Over-the-Air) updates. It will be necessary to bring out the SWD interface on the PCB to enable programming the module with Nordic's nRF Connect SDK which uses the Zephyr RTOS platform. Once the Bootloader and/or FOTA firmware have been loaded to the module it should be possible to load future firmware updates via the UART or FOTA methods. See the Nordic DevZone for additional information on Bootloader and FOTA firmware options.

Datasheet - BL5340 Series
Datasheet - BL5340PA Series