The motherboard or chipset doesn't have a "NVMe version" since NVMe mainly defines just the commands, not the physical link – and the commands are generated by your OS, not by the motherboard – so the NVMe version or feature support depends entirely on the OS.
(Sure, the motherboard's firmware has to speak some NVMe when booting the OS, but it only needs the most basic 1.0 for that purpose.)
For example, the standard Windows NVMe driver has some NVMe 2.x support – though most of that is server-only features which have no impact on regular M.2 SSDs on a regular PC. Intel's RST/VMD driver might support different features.
NVMe SSDs use a standard PCI-Express connection for the physical link, so the connection speed depends on the PCIe version supported by the M.2 slot (and by the SSD itself); not so much on the NVMe version. For example, "Gen3 SSD" really refers to PCIe Gen3 (currently there is no such thing as NVMe version 3).
You should be able to see the effective PCI Express link speed (PCIe version and lane count) for each device in HWINFO or other tools. Your HM770 is compatible with PCI Express Gen4 in general, although whether it is available for the M.2 slots will depend on the specific motherboard.