Lain is not about “a digital identity that *seems* more real” or about “*feeling* that your identity is [anything, much less constructed with intention by an outside agent]”. It’s an ontological analysis of identity as such. You missed the point.
Paranoid or sad is mostly irrelevant, though paranoid is slightly more apt. Again though, the art itself has a status of <feeling>, it’s not about <feeling>-inducement in the audience.
Also clearly it’s fine to interpret aesthetic experiences however you wish, but the more straightforward interpretations of lain are pretty uninspired and drab