If I intend to perform iʿtikāf in al-Masjid al-Ḥarām during the last ten days, but I leave the masjid to go to a hotel and then return, or stay within the boundaries of Makkah, does my iʿtikāf remain valid, or is it invalidated by leaving the masjid?

Leaving the mosque to sleep in a hotel breaks and invalidates iʿtikāf, because staying overnight inside the mosque is a condition for maintaining the iʿtikāf. It is not permissible to leave except for unavoidable necessities, such as relieving oneself (using the restroom), performing ghusl if the facilities are not available in the mosque, or bringing food if there is no one to deliver it to him.