This is “a voiceless w, as in English white (in northern pronunciation)”
according to Appendix E of The Lord of the Rings, and so we copy the
[[w#]] phoneme from the English phonemes. I can’t actually hear much of
a difference from the previous [[hw]] (I know what the difference
between [[w]] and [[w#]] should be, but [[hw]] already sounds like
[[w#]] to me), but at least this improves the --ipa output, changing it
from [hw] to [ʍ].

We used to inherit it from the Latin phonemes, which, as I noted in the
commit adding the Sindarin diphthongs, sounds more like /ae/ than /ai/.
Copy the phoneme from Sindarin so that it sounds like /ai/, not /ae/.
(There is no ⟨ae⟩ diphthong in Quenya, so we don’t need a copy of that.)

I’m not aware of any statement by Tolkien to this effect, but it just
seems natural to me, and the [ŋ] is at least found in the Omikhleia
Sindarin dictionary [1] (e.g. entry tinc, [tˈiŋk]).

Based on a similar phoneme rule in ph_english.

[1]: https://www.jrrvf.com/hisweloke/sindar/index.html

Both are copied from the Finnish phonemes, since Finnish was a major
inspiration for Quenya. This means that the ⟨iu⟩ diphthong is a
“falling” one – according to Appendix E of The Lord of the Rings, this
is the original pronunciation, but by the Third Age (the time in which
The Lord of the Rings is set) it had become a “rising” one, so I may
change the phoneme later, not sure.