What is the ruling for carrying a stitched bag that is tied around the waist of the pilgrim to keep his shoes and other necessary items, whether inside or outside the Sacred Precinct, while observing the rites of pilgrimage (ihram)?

Ihram is one of the pillars of Hajj
Islamic law laid down certain conditions for ihram, either for hajj or for ‘umrah. One of those conditions is that a pilgrim should not wear any sewn garments. Sewn garments are those that are designed to fit the body or a part of it and whose pieces are sewn together by thread or something similar.

The ruling
The bag mentioned in the question is not designed to fit a specific part of the body, but is for carrying the pilgrim's personal belongings. It does not fall under the category of sewn items which are prohibited and is therefore permissible to be carried both inside and outside the Sacred Precinct.

And God Almighty knows best