Aligned glosses with ない

I don't see how that note does anything meaningful. Yes, the 終止形 is also the 辞書形, but なし is the predecessor to ない, not a form of ない.
なし itself is a standalone word woth its own inflectional paradigm. We also don't have such a note on 青し or other ク形容詞 for that matter.

@@ -35 +34,0 @@
-<s_inf>old terminal form of 無い</s_inf>
@@ -36,0 +36 @@
+<gloss>not being (there)</gloss>

I don't think that etymological note in sense 1 helps much.

@@ -20 +19,0 @@
-<s_inf>derived from adjective 無し</s_inf>

Not quite true, many words have no traceable origin of any kind other than themselves; in Japanese this actually happens far more often than, for example, in english where most words have a traceable history in some combination of semantics, morphology, and phonetics. In contrast to this, every other 五段 verb, noun and particle shows little to no such alterations.
Now, here, the information the note provides is both a distinction and a connection in between sense 1 and 3: a reader looking at this entry, or even finding the variants separately, will surely make a connection between them as they look the same, sound the same, and the meanings are notably similar; the aim of the note is to clarify what that relation is rather than to simply leave the reader to their speculation.

In summary, since a shared etymology among the senses is already strongly suggested, the note is there to clarify what that etymology (if any) is to any reader who might be left wondering.

@@ -20 +20 @@
-<s_inf>derived from old adjective 無し</s_inf>
+<s_inf>derived from adjective 無し</s_inf>

無し: derived from 無し

How is it helpful? All words have an etymology, that doesn't mean they all benefit from having notes on it.