Julie Leslie, the author of The Perfect Wife, which is a translation of/commentary on Strīdharmapaddhati (Guide to the Religious Status and Duties of Women) by Tryambaka of 18th century Thanjavur, says:
The maṅgalasūtra, the auspicious thread on which beads (usually
black or gold) are strung, is fastened around the neck of the bride
by the groom during the marriage ceremony (cf. PVK II.i.537).
Chapter XV of the Laghvāśvalāyanasmṛti describes the sacrament
of marriage in detail and provides the earliest reference to the
marriage thread (māṅgalyatantu, v.33; Dh.kośa III.iii.p.2048).
Mantras are recited to ensure the wife's fidelity to her husband
and Gaurī bestows saubhāgya on the bride. Saubhāgya originally
and literally meant 'good fortune' or 'prosperity', but it came to
have as its established meaning (virūḍhalakṣaṇā) the good fortune
of the happily married woman whose husband is alive. The prefix
sau, with which the married woman is addressed, stands for saubhāgyavatī, meaning 'fortunate woman' (i.e. by virtue of her marriage;
Baudh.gṛ.I.6.30). The maṅgalasūtra, the tilaka, and the red line
of sindūra in the hair, are all indispensable signs of the married
woman whose husband is alive; as long as he lives, they must be
Re: Toe-rings, quoting Anant Sadashiv Altekar, she says:
Nose- and toe-rings seem to be another late development. Altekar
notes the conspicuous absence of the nose-ring in sculpture and
painting throughout India before the Muslim invasions. He
concludes that it was originally a Muslim ornament (1978:301 ff.;
cf. PVK II.i.537). By the time of Tryambaka, however, it was
another indispensable sign of saubhāgya.
So, it's possible Sītā and Draupadī wore the maṅgalasūtra but not nose- and toe-rings.