whether Shaivas and Shaktas think themselves as part of Advaita's
pancayatana or they also oppose Advaita and have separate sampradayas?
Shaivas and Shaktas follow different philosophies and consider themselves different sampradayas with respect to Smartas.
Shaktas Follow their own version of Advaita (ShAktAdvaita) where Brahman is also considered satya and Jagat is also considered satya. As shown below The Sakta Acharya Bhaskararaya rejects the Jagat mithya concept in his Lalita Sahasranama Bhasya which is one of the distinguishing features of Kevala Advaita.
The Shaivas, similarly go by their own schools of thought, some of which are enumrated as follows-
1. Viśēṣādvaita/विशेषाद्वैत
The Vyutpatti of Viśēṣādvaita śabda is “विश्च शेषश्च विशेषौ ईशजीवौ तयोरद्वैतं विशेषाद्वैतम्" . The meaning of this is "विश्चक्षुषि व्योम्नि वाते परमात्मनि पक्षिणि" (एकाक्षरकोष, पृ.१८) from Nighaṇṭū it's clear that the meaning of "वि" śabda also happens to be Paramātmā. From the Vyutpatti of "वाति उत्पादयति जगदिति विः " it's evident that the "वि" śabda signifies the Kāraṇībhūta Īśvara of the Jagat. Though Amarakōṣa says that the meaning of "वि" śabda is Pakṣī anyways in Mundaka Up. Paramātmā is described as Pakṣī "द्वा सुपर्णा सयुजा सखाया" (मुण्डको. ३।१।१). So the actual meaning of "वि" śabda should be taken as Paramātmā. Śēṣa śabda denotes Paramātmā's aṃśaroopa ie Jīvātmā. "यथाऽग्नेः क्षुद्रा विस्फुलिङ्गाः" (बृहदारण्यको. २।१।२० ) thus from this Śruti (अग्निकण के दृष्टान्त से) it's proved that Jīvātmā is aṃśa of Paramātmā. By Aṃśāśībhāva it's established that inbetween Jīva and Paramātmā "यथा नद्यः स्यन्दमानाः " (मुण्डको ३१२१८) this śruti denotes the Advaita (Abheda) bodha . In the context of the world, this Siddhānta that asserts the non-differentiated state(Abheda) of 1. Shiva and the liberated state of the soul(jīva) is called "Viśēṣādvaita".
विशब्देनोच्यते शम्भुर्हंसहंसेति मन्त्रतः । शेषशब्देन शारीरो
यथाग्नेरिति मन्त्रतः । । अद्वैतेन भवेद्योगो यथा नद्य इति श्रुतेः ।
(श्रीकरभाष्य,मङ्गलश्लो. १६)
In this verse, The Saiva acharya Śrīpati Panditā has succinctly explained the essence of Viśēṣādvaita.
2. Śivādvaita/शिवाद्वैत
The Vyutpatti of this śabda is “शिवश्च शिवश्च शिवौ, तयोरद्वैतं शिवाद्वैतम्”.First, the śabda "शिव" denotes the Paramātmā, and the second śabda "शिव" represents the individual soul(jīvātmā) that is a part (aṃśa) of the same. In the state of the world, the principle of Śivādvaita Siddhanta is to describe the non-dual state (Advaita/Abheda) present in both the worshiped(Śiva) and the worshiper(Aṃśa of Śiva) as the liberated state(Muktāvasthā).
3. Śaktiviśiṣṭādvaita/शक्तिविशिष्टाद्वैत
“शक्तिश्च शक्तिश्च शक्ती, ताभ्यां विशिष्टौ शक्तिविशिष्टौ शिव - जीवौ तयोरद्वैतं शक्तिविशिष्टाद्वैतम्” according to this Vyutpatti the Siddhānta that denotes Abhēda ie Advaita b/w Sarvajñatva Sarvakartrutva etc Sūkṣmacid- Cit-śaktiviśiṣta Śiva and Alpjñatva Alpakatrutva etc Sthūlacid-citśaktiviśiṣta jīva that very siddhānta is known as Śaktiviśiṣṭādvaita Siddhānta. This Siddhānta is derived from Bhramara- Kīṭa Nyāya. Just as a kīṭa , distinct from a bhramara, transforms into a bhramara through constant meditation on the bhramara, similarly, an individual (jīva) with a vastly different nature from Śiva also attains the svaroopa of Śiva through continuous(nirantara) meditation on Śiva, developing their latent Śaktis. This is the essence of Śaktiviśiṣṭādvaita Siddhānta.