Please see this Nexus site news article for details.
A Working "unofficial" fix (confirmed) to login to Nexus with MO (v1) or older NMM versions without updating is available in this Reddit thread: Classic Login fix for MO1/NMM.
However, just unpacking the NVSE archive package to the "Fallout New Vegas" folder may not create a "Data\NVSE" folder or the "Data\NVSE\Plugins" sub-folder upon installation unless you tell it to include sub-folders when doing so. It definitely does not create a configuration file or automatically enable it's log files (which will be found in the game's root folder).
You need to do so yourself, using any plaintext editor such as Windows Note Pad.
Supplemental NVSE Plugins such as JIP, Lutana, MCM, NVAC, or NVSR should go into the "Data\NVSE\Plugins" folder.