Is there support for the GeForce 700M Series, specifically the GT 740M, for Vulkan?
Yes. The 740M is well supported by the current 440.64 driver, including Vulkan.
The 440 driver does not seem to support the 700M series: https://download.nvidia.com/XFree86/Linux-x86_64/440.31/README/supportedchips.html
Ignore the README, it is only valid for Windows, there mobile Keplers like the 740M are only supported up until v425. On Linux, the latest 440.64 driver works.
When I try to download through the website it shows that the latest supported versions are 418 for long term and 415 for short term
The website has many failures when searching for the correct driver for linux. Just ignore.
Always just use the packaged drivers provided by your distro’s repositories.