How would you account for the usual writing of 𓇓𓏏𓈖 with the ⟨n⟩ written last? With the reading 𝘯(𝘫)-𝘴𝘸𝘵 "he of the sedge plant," it is typically explained as a kind of honorific transposition.
(I am still surprised whenever I see a particularly old article transliterate the word as 𝘴𝘸𝘵𝘯.)

Is the 𝘣𝘫𝘵 in that sentence an infinitive then? Of which verb?

The verb 𝘣ȝ "have power" is a 2-rad. verb and wouldn't typically have a final -𝘵.

Are there other words in which 𓆤 (L2) is used as a phonogram/phonetic sign? Thot Sign List has it primarily as a logogram/classifier: thotsignlist.org/mysign?id=16

Are you suggesting a later reanalysis/folk etymology after phonological mergers? Or a new etymology?

The sparrow 𓅪 was used as a semantic classifier on words relating to being little, such as 𝘯𝘥̱𝘴 “small,” and also by extension negative words such as 𝘣𝘫𝘯 “bad” or 𝘮𝘳 “ill.”

Egyptologists often call this sign the “bad bird.”

The Egyptian word for flamingo was 𝘥𝘴̌𝘳, literally “red (one),” due to its characteristic color.

Because of this, the flamingo 𓅟 is used as a triliteral phonological sign representing ⟨dšr⟩, usually found in 𝘥𝘴̌𝘳 “red” and related words.

A falcon on a standard 𓅆 was commonly used as a semantic classifier (or “determinative”) after divine names.

This is because 𝘏̣𝘳(𝘸) /ˈħaru(w)/ ("Horus," Greek Ὧρος), who was depicted as a falcon or falcon-headed being, served as a prototype deity.

The quail chick 𓅱, also a phonological sign, was used for ⟨w⟩ /w/.

This sign is often found at the end of words because the standard plural endings in Ancient Egyptian were -𝘸 and -𝘸𝘵 for masculine and feminine nouns, respectively.

The Egyptian vulture 𓄿 is used as the phonological sign for ⟨ȝ⟩ (Egyptian 'alef').

In the Old Kingdom, this sign probably represented a uvular trill /ʀ/, but by the Middle Kingdom, the underlying sound had shifted to a glottal stop /ʔ/.

All this is to say—there does not seem to have been a native Egyptian phrase that meant “blue sky.”

But if we *really* want to force it, I would probably lean towards something like 𓊪𓏏𓇯𓍿𓎛𓋥𓈖𓏏 𝘱𝘵 𝘵̱𝘩̣𝘯𝘵 “gleaming sky” or “sky of faience.”

Coincidentally, the classifier for 𝘵̱𝘩̣𝘯 𓋥 (S17), which probably represents a pectoral made of faience, has a variant that appears in Dynasty 18, 𓋣 (S15).

What is that element at the top of the new sign? That’s right, it’s the 𓇯 𝘱𝘵 “sky” sign!

Faience is certainly close to the color of a blue sky.

As an illustration, here is a Late Period inlay of the 𓇯 𝘱𝘵 “sky” sign (N1) made of faience, now in the Metropolitan Museum of Art, New York (26.3.164i).

A much later Ptolemaic text at Karnak uses the phrase 𝘱𝘵 𝘴𝘵𝘫(𝘵) 𝘮 𝘵̱𝘩̣𝘯(𝘵) “the sky, radiating with faience” (Opet 147.2).

The word for “faience” 𓍿𓎛𓋥𓈖𓏏𓈒𓏥 𝘵̱𝘩̣𝘯𝘵 is derived from the verb 𓍿𓎛𓈖𓋥 𝘵̱𝘩̣𝘯 “to gleam, dazzle.”

Instead of using a traditional color words, Egyptians sometimes spoke of the sky using words that expressed [ʙʀɪɢʜᴛ], [ꜱʜɪɴʏ], or [ᴄʟᴇᴀʀ].

An early example in the Pyramid Texts is 𝘫ꜥ 𝘩̣𝘳 𝘱𝘵 𝘣ȝ𝘲 𝘱𝘥̱𝘵 “The face of the sky has been washed. The expanse is bright/clear” (PT 570 §1443a).

So what word(s) did Egyptians use for the color of the sky? As far as I have been able to find, they…didn’t.

For example, although 𝘸ȝ𝘥̲ “green” overlaps a bit with what we consider blue, it (as far as I can tell) is never used to describe the sky.

This isn't too surprising, as classification of colors is very culturally determined.

The most famous example of this is probably the Homeric Greek expression οἶνοψ πόντος “wine-faced sea.” As a comparison, Egyptians called the sea 𝘸ȝ𝘥̱-𝘸𝘳 “Great Green.”

The easy part—the Egyptian word for ”sky” was 𓊪𓏏𓇯 𝘱𝘵 (→ Coptic ⲡⲉ / ⲫⲉ) , also sometimes translated more poetically as “heaven(s).”

“Blue” is more difficult, as the Egyptian languages don’t really have a word for what we call “blue.”