Which mantras (in metres other than Gayatri) are prescribed for the Sandhya of Non-Brahmins?

Question

It is said that one must follow the mantra in Gayatri metre of the Upasya (generally main Gayatri), granted by the Guru. There’s a whole list of them in the Taittiriya shakha. There also seems to be a Pauranika Sandhya Vidhi open to all Hindus, not initiated, in which too the mantra prescribed is the Gayatri, but without the Vedic accents. However, I have come across a reference where the Gayatri metre is only for Brahmins.

As per the Śāṅkhāyana Śrauta Sūtra XIV.33:

The Brahmins have the Gāyatri as their metre... (9). The Kṣatriyas have the Triṣṭubh as their metre...(12). The Vaiśyas have the Jagati as their metre...(15). The Śudras have the Anuṣṭubh as their metre...(19)

As per Baudhayana:

A Brahmin must be initiated in Spring, a Kṣatriya in Summer, a Vaiśya in Autumn, a Rathakāra in the monsoon or all in Spring.
-Gṛhyasūtra 2.5.6

Let him perform the initiation reciting, according to the order of the varnas, a Gāyatrī, a Triṣṭubh, a Jagatī verse.
-Dharmasūtra Praśna I, Adhyāya 2, Kaṇḍikā 3 verse 11

As one can observe, each Varna must be initiated by the Guru using a different metre, prescribed for their Varna. The Gayatri mantra (being in the Gayatri chhanda) is therefore to be used only by Brahmins. Accordingly the following questions:

Questions

1. With which mantras (in their respective metres) are the Varnas usually initiated (usually use) and who is the rishi and devata to be worshipped?
2. In case of the special Upasyas (as per Taittiriya Shakha), do the same Upasyas have mantras in all the 4 metres or only the Gayatri?
   
   ^{So for example if one is a Vaishnava, are there Vishnu Trishtubh, Jagati and Anushtubh also, if not then all 4 varnas can’t have the same Upasya Deva which is little odd. Please also explain whether Gayatri Devi (as an Upasya) has the other 3 metres}
3. In the Pauranika Sandhya Vidhi (supra), should an uninitiated person use the Gayatri or should one use the respective mantras (as answered in Q1 here) as per one’s Varna, without the Vedic accent?

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Please focus the answer MAINLY on KSHATRIYAS AND VAISHYAS, without contending Shudra’s allowability. While answering just mention the mantra if possible

^{Note on Rathakara and Shudra. Rathakara’s status is disputed in different texts. But they’re not among the top 3. Going by Manusmriti 10.41, they can be equated with Shudras and thus for initiation be given the Anushtubh metre meant for Shudras. (I’m not contending on initiation about ALL Shudras. Only about the Rathakara’s metre and mantra). Not duplicate}