Isn't covering a woman's face and wearing the niqab and gloves during prayer more important than covering it when leaving the house, by analogy with a woman covering her feet during prayer, if the niqab is obligatory?

It is not correct to compare the covering of a woman's face in prayer to the covering of her feet, because there is a consensus (ijma') on the permissibility of a woman uncovering her face in prayer, and an analogy (qiyas) that contradicts consensus is invalid. Furthermore, a worshipper is required to place their forehead directly on the ground, which is why scholars disliked a woman covering her face in prayer, unlike the feet and knees, which are not prescribed to be uncovered. As for the hands, scholars have differed on whether they are considered 'awrah (parts of the body that must be covered).