Disclaimer.: It's gonna be a long answer.
Both, Brihaddevata and Yajurveda story looks similar to me with Bhagawan Rudra destroying the TriPuras with some symbolisms.
From the Vedic point of View.:
In this answer of mine, i have mentioned how Vedik Indra = Rudra.
Yajur Veda 6.2.3.:
The Asuras had Tripuras; the lowest was of iron, then there was one of silver, then one of gold. .
'By siege they conquer great citadels.' They made ready an arrow, Agni as the point, Soma as the socket, Visnu as the shaft. They said, 'Who shall shoot it?' 'Rudra', they said, 'Rudra is fierce, let him shoot it.' He said, 'Let me choose a boon; let me be overlord of Pashus.' Therefore is Rudra overlord of Pashus. Rudra let it go; it cleft the Tripuras and drove the Asuras away from these worlds.
Bṛhaddevatā of Rig Veda, Ch. 7.:
Having shattered with the might of his arm the citadels of gold, silver, and iron, (and) having slain all (of them) in their respective spheres (yathāsthānam), as arrayed on earth and the other (two worlds). On earth he exterminated both the Kālakeyas and the race of Puloma, the archer, and in heaven the notorious (tan) offspring of Prahlada.
Kaushitki Aranyaka of RigVeda.:
To him then Indra said: . . Transgressing many compacts I killed the people of Prahlada in the sky, the Paulomas in the atmosphere, the Kalakanjas on the earth. Of me, such as I was then, not a single hair was injured. . .
III-2. Then he (Indra) said: I am the Spirit of the vital breath (prana), the intelligent Self (Atman). As such, worship me as life, as immortality. . .
So, From the above verses, it's clear that Lord Indra Killed Rakshasas in three Puras and shattered them. The 3 Puras being - The lowest, Iron viz Earth, middle being Silver viz Atmosphere and the highest being Gold aka Heaven.
Before, moving on ahead let me just share a small point about names. The names of deities are nothing but their attributes (gunas).
For its (Brihat) Big nature is called Brahma.
For its All pervasive (Vishva) nature is called Vishnu.
For its nature of being Fierce, bringing and taking away tears cries (Rudan) is called Rudra.
For its nature of being a Ruler (Ishana) and being Self Realized (Idandra), it's called Indra and so on.
Katha Aranyaka of Rig Veda, 2.100.:
Indeed the deva-s did not recognize Rudra who had entered the heavenly world wandering in with a solar luster. They said: “Who are you?”. [He replied]: “I am Rudra, I am Indra, I am the Āditya, I am the arrival of all the divine luster. They said: We shall not offer a share to this one [i.e. Rudra]. Roaring he [Rudra] yelled at them. He rushed at them. They [the other deva-s] said: “Sir, you are all of this”. Because roaring he yelled at them that is Rudra’s fierceness (rudratvam). Because they called him sir (bhavān) that is Bhava’s lordship over existence. Because they said you are all this that revealed Śarva’s [prowess] as an archer. 𝗕𝗲𝗰𝗮𝘂𝘀𝗲 𝗵𝗲'𝘀 𝗲𝘃𝗲𝗿 𝗯𝗹𝗶𝘀𝘀𝗳𝘂𝗹 𝗮𝘀 𝗲𝘁𝗲𝗿𝗻𝗮𝗹𝗹𝘆 𝗵𝗲'𝘀 𝗯𝗲𝗻𝗼𝘃𝗲𝗹𝗲𝗻𝘁 𝗳𝗼𝗿𝗺 𝗼𝗳 𝗦𝗵𝗶𝘃𝗮.
Now, let's understand.:
Q.: How, Indra Shattered the Puras.?
A.: By the might of his arms (स्ववाहुवीर्येण).
Q.: Why, the devas asked Rudra to to shoot the arrow.?
A.: Because Rudra is fierce (क्रुरः).
So, the Bahu (Arm) Veeryam (Might) of Indra is his Rudrattva.
Just, as the Rudrattva of Bhagawan Shiva is Lord Veera Bhadra, Kala Bhairava, etc.
Sri Linga Purana 1.72.:
The king of mountains (Himavān) was his bow and the bowstring was the (भुजंगाधिपः) lord of serpents (Vāsuki) himself, along with Kālarātri (the night of nightmares) and Indradhanus (rainbow).
The bell of the bow was goddess Sarasvatī of the form of the Śrutis (Vedas).
So, Pinaka was created by Using all kinds of Kings viz Himavan/Mandara as the bow stick and Vasukhi, Kalratri and Indra Dhanush as bow string. So, it's also called Indra Dhanush the Lord/King of the Bows.
Atharva Veda 15.1.:
He (Eka Vratya/Shiva) is the only ruler of the Vratya group, The bow which was touched (held) by him was called Indradhanush. 6.
Again, the Indra Dhanush is Indra himself and the 7 colours of it can be equated with how Indra (Indriya/Prana) divided itself into 7 Purushas after churning as mentioned in Shatapatha Brahmana 184.108.40.206&6.
I have mentioned Indra Dhanusha in details in this answer of mine.
Now, Shatapatha Brahmana in 220.127.116.11 mentions how Prana is Indra being the Indriyas.
Just a side note.:
The snakes are called Bhujanga. Bhuja (Coiled) + Anga (Limb/Part) and Adhipa is King same as Adhipati.
Bhuja can also mean Arm and Indra is King's synonym. So, if we translate the above Linga Purana Bowstring verse with changed words it becomes something like this.:
The Arm (Bhuja) part (anga) of Indra (Adhipa) became the bow string.
Indra is our Antaratma. Being the ego/ahamkara (I)-ness (Aham) in us as Asani.
B.G. 13.23, Mundaka Up. 3.1.1-2 n 3.2.9, states how our body have 2 atmas 1 Jivatma and other Paramatma (Maheshwara) and Jiva remains stuck in sansara but after realising the Paramatma it becomes paramatma itself. Aitreya Up. 1.3.13-14 also states that this Self realized Jiva is nothing but Idandra aka Indra as I have already mentioned in this answer of mine.
So, when we say Aham Brahmasmi it's same as the self realisation of Indra being I(Indra/Jiva) is Brahman.
The Process for Indra for becoming Brahman is Tripura Dahan.
Let's study the Bow of Rudra first.
The Bow is the Mountain, String is the Snake, Bells are Vedas.
So, our Spine being the meru mountain and the Kundanini being the snake which goes from lower end of the bow to the upper. Bells represents the nada omkara which a yogi heard after piercing the 3 puras which are actually the 3 knots Brahma Granthi in Mooladhara Chakra, Vishnu Granthi in Anahata Chakra and Rudra Granthi in Ajna Chakra after that he reaches Sahasrara and becomes Brahman himself there. As i have mentioned in this and this answers of mine. 3 granthis are gates for crossing 3 Shariras or Dehas the sthula, sukshma, and karana or 3 states Jagrat, Swapna and Sushupti.
Again, this Jiva is also Parmeshwara himself as i have mentioned in this answer of mine.
Same is the concept of Samudra Manthan. Stick being the Mandara, Rope being Vasukhi, and support (Mooladhara) being the Tortoise (Kurma/Kashyapa/Prajapati) and the 3 puras being the 3 gunas Sat, Raj and Tam as i have mentioned in this answer of mine.
Q.: Why Indra, Agni and Vishnu are called Purandra.?
A.: 1. Because they formed the weapons for killing Tripuras.
- Indra (Prana) and Agni along with Kundalini goes from Mooladhara to Sahasrara, after crossing the 3 granthis in inner cismos. And as for Vishnu being the male form of Uma/Kundalini takes 3 steps in 3 Puras (Earth, Air, Heaven) in outer cosmos as mentioned in this and this answers of mine.
Conclusion.: Lord Indra (Jiva/Pashu) crosses 3 puras to get free from Pasha (Maya) and thus reaches Bhagawan Pashupati and becomes Ishana/Ruler (Ishwara) himself.
Vak being the Indriya is also Prana/Rudra as mentioned in Chandogya Upanishad and this and this answer of mine. So, Vak/Atma Shuktam where both Rishi and Devata both being Vak Devi is a Self Realising Shuktam.
Rig Veda 10.125.6.:
“I bend the bow of Rudra, to slay the destructive enemy of the Brāhmaṇas, I wage war with (hostile) men. I pervade heaven and earth.”
Explanation.: I (Indra/Vak, being the bow string/Kundalini) bend the bow of Rudra . . . I pervade/Penetrate Earth, (Air), Heaven (and go beyond).
I hope this clarifies all your queries. Prd..