Does the incident of Omar seeking the Prophet’s permission and women initiating the wearing of the hijab indicate that the niqab was known but not obligatory for them at that time?

This hadith (definition) does not indicate the permissibility for a woman to uncover her face in front of non-mahram (definition) men. The women mentioned are the Mothers of the Believers, who were asking for an increase in their maintenance. If they were not, then it is probable that the incident took place before the فرض of the hijab (definition), or that the Prophet was astonished by their swiftness in veiling themselves before Umar's permission. Furthermore, looking at a woman's face and being in seclusion with her were specific privileges of the Prophet, peace and blessings be upon him.