Are there verses praising Siva as residing within the Sun like there are statments for Vishnu regarding the same?
The Sun which is seen in the sky above is directly told as having darshan of Lord Shiva in Veda Samhitas. In the first Anuvaka of Sri Rudram we have:
असौ यस्ताम्रो अरुण उत बभ्रुस्सुमङ्गलः । .... असौ योsवसर्पति नीलग्रीवो विलोहितः । उतैनं गोपा अदृशन्नदृशन्नुदहार्यः ॥ उतैनं विश्वा भूतानि स दृष्टो मृडयाति नः ॥ (Yajurveda 4.5.1)
This Sun who is copper-red when he arises, then golden-yellow, this highly auspicious and beneficent one is truly him. The Nilagriva Rudra who has assumed the form of the sun that glows red when rising. Him the cowherds, the women carrying water, and all the creatures behold. He, who is seen by all, let Him send happiness to us.
Similarly in the Brahmanas of Vedas as described in this answer.
He answered, ‘ You are Mahadeva’ Since the sun is Mahadeva, thereby the Mahadeva harms him not, nor his offspring, nor his cattle, nor any one claiming to he his.... (Rigveda Kausitki Brahmana chapter 6)
Similarly in Upanishad also like:
यो वै रुद्रः स भगवान्यश्च सूर्यस्तस्मै वै नमोनमः ॥ ७॥ (Atharvasiras)
He who is Rudra, He is Bhagavan, He is in the form of Sun, Salutations to him
Similarly in multiple Puranas as described in this answer.
रुद्र इत्युच्यते देवैर्भगवान् भुक्तिमुक्तिदः । सूर्यात्मकस्य रुद्रस्य भक्तानां भक्तदायिनः ।। सुवर्चला स्मृता देवी सुतश्चास्य शनैश्चरः । समस्तसौम्यवस्तुनां प्रकृतित्वेन विश्रुतः ।। (Linga Purana)
The Lord in the form of Sun is called Rudra by the Gods. In the form of sun he bestows prosperity to all and yields all the worldly pleasures and salvation. When he becomes Sun then his Godesses is Suvarchala and their son is Saturn (Sanaishchara).
सूर्यों जल मही वहिर्वायुराकाशमेव च। दीक्षितो ब्राह्मणः सोम इत्येतास्तनवः क्रमात्॥७॥ सुवर्चला तथैवोमा सुकेशी चापरा शिवा। स्वाहा दिशस्तथा दीक्षा रोहणी च यथाक्रमम् ॥८॥ (Vishnu Purana)
He also assigned to them their respective stations, the Sun, water, ether, air, fire, earth, the ministrant Brahman, and the moon; for these are their several forms. The wives of the Sun and the other manifestations, termed Rudra and the rest were respectively, Suvercalā, Uma, Vikesi, Sivā, Svāhā, Dišā, Diksā and Rohiņī.
Yes, Bhagawan Shiva reside in the Sun plus he is also the Sun as we see it.
"He said to him, 'Thou art Îsâna (the Ruler).' And because he gave him that name, the Sun became suchlike, for Îsâna is the Sun, since the Sun rules over this All. He said, 'So great indeed I am: give me no other name after that!' (Shatapatha Brahmana 6:1:3.17).
Then, [worship of the effulgent being in the sun]: The white glow of the sun is sā, and the dark bluish-black glow is ama. These two together make up the word Sama.There is a deity within the orb of the sun, who is seen by the yogis. His whole body glitters like gold, even to his toe-nails. He has a bright golden beard and bright golden hair. (Chandogya Upanishad 1.6.6).
Salutations again and again to the Golden armed, to the the golden hued One, whose form is resplendent like Gold, who is the Lord of Gold, who is the Lord of Ambika, of Uma, who is the Lord of Pashus”~ (Taittiriya Aranyaka 10.22.1).
I know the great Purusha (Rudra), who is having sun like luster and is beyond darkness. Only by knowing him one overcomes death, there is no other way to supreme goal. (Svetasvatara Upanishad 3:08).
When there is complete absence of the darkness of ignorance, then what is experienced is neither day nor night; neither existence or non-existence; the Supreme Lord Shiva alone exists as pure; that is indestructible; that is adorable light and the deity of even Savitar (Sun) himself; from that this ancient wisdom proceeded all over the world”. (Shvetashvatara Upanishad 4.18).
“This Sun who is copper-red when he arises, then golden-yellow, this highly auspicious and beneficent one is truly Rudra. These other Rudras who are quartered round about in all directions of this earth, may I ward off their anger by my praise”. (Yajurveda Sri Rudram – Anuvaka -1).
“The black-throated Rudra who has assumed the form of the sun that glows red when rising. Him the cowherds, the women carrying water, and all the creatures behold. He, who is seen by all, let Him send happiness to us”. (Yajurveda Sri Rudram – Anuvaka -1) .
For more you can see this answer of mine.
I hope this clarifies all your queries. Prd..