Yes, Goddess Parvati is Raj Rajeshwari Bhagwati Lalita Tripurasundari.
Maa Tripurasundari is more transcendental and when she incarnates in this realm as the daughter of King Himavan, she is known as Parvati.
Tripurasundari is the most beautiful among the three realms. Basically she is the Ultimate source of beauty, the entire beauty, whatever is beautiful, it's her manifestation.
She is also known as Kamakshi, she is the consort of Kameshwar Mahadev but Mahadev also resides with him in multiple forms like Mahesh, Rudra, Bhairav, Ishan, not just as husband (Kameshwar) but also in these forms to serve her out of love.
She sits on Sadashiva, another auspicious form of Mahadev. This symbolizes the active, flowing energy, i.e., Shakti over the static, unshakable consciousness, i.e., Shiva. Mahadev is the Aadhar (Base) and Mahadevi is the projection.
Jai Maa Lalita Tripurasundari 🙏 Har Har Mahadev 🙏