Is this historically just a different form of the Tantric goddess herself or is described as “satvic” take on her?
There is no Satwik, Tamasic or Rajasic Chinnamasta as opposed to Tara. Indeed Jogani devi and Chinnamasta devi are one and the same.
Is there different stories and mythology for her ?
No the kathamrit for Chinnamasta and Jogani are same.
Seems like such a strange juxtaposition of cheerful dance like that w/ self-behead image 😵
That isn't any normal dance just for merry moments. Garba is originally the Lasya Nritya that Bhagwati loves herself. Thus even one of her Sahasranaam mentions her to be,
The one who loves Lasya (Garba)
Coming to the point that how can people approach such a fearsome deity without proper initiation and Guru's guidance?
This is because she is venerated as Kuldevi. Thus, worshipping Kuldevi as per Lokachara by the people in clan is must. In such cases Lokachara and the puja padhati followed in family over writes Shastras.
Scriptures support use of Lokachar in such cases.
Arthashastra of Vishnugupt Chanakya,
Those who don't know Deśāchāra are fools and know nothing.
Brahmavaivart Puran, Ganapti Khand, chapter 7,
वेदाचाराल्लौकिकाचारो बलवान् यथा पार्व्वत्युवाच । केवलं वेदमाश्रित्य कः करोति विनिर्णयम् ।
बलवान् लौकिको वेदाल्लोकाचारञ्च कस्त्यजेत् ॥
Devī Pārvatī says who else has the capability to leave Lokāchara which is as important as Vedas.
But this doesn't means one can do her Pratyakshikaran merely by following lokachar and Bhakti. One can only earn abit of her grace that's all. For getting pratyaksha darshana of Amba indeed, a proper initiation and Guru parampara is must.
Thus, many Gujaratis worship her as their Kuldevi and yet face no grave consequences. But, the person who doesn't belongs to that clan might face her wrath.