Is it impermissible for women to run/jog between safa and marwa (during hajj/umrah saee)?

According to the Islamqa women do not run between safa and marwa as it may lead to immodesty.

Women, however, do not run, because they are required to cover themselves and be modest, and running may expose their bodies and their charms

Furthermore they say:

Ibn al-Mundhir said: The scholars are unanimously agreed that women do not have to trot around the Ka’bah or between al-Safa and al-Marwah

From my understanding, Islamqa suggests its not obligatory for the women to run/jog.

1. Is it impermissible for her to run/jog out of remembrance for Hajar ? (provided she can manage to not uncover)
2. if yes, is it a sunnah(rewarding) if she runs/jogs?

I haven’t found a prohibition from Hadith hence my question since the very act men are mimicking was done by a woman (Hajar).

(Looking for Sunni answers)