What is the Sharia's opinion on the Hajj deposit with a solidarity return, where half of its proceeds are invested to enable shareholders or those under their guardianship to perform Hajj, and the remainder is distributed to shareholders as a return?

So long as these contributions are governed by the Sharia (definition)-compliant regulations in their collection, accumulation, investment, and disbursement, then there is no legal impediment to them. Rather, they fall under the category of cooperating in righteousness and piety. Allocating half or any agreed-upon percentage for Hajj or other acts of righteousness, with the remainder distributed based on the capital or administrative expenses as per the agreement, is permissible.