Is it permissible to rent a shop and equip it, then lease it to a resident foreigner, giving him the choice between working for a salary or otherwise, knowing that this is systematically prohibited in Saudi Arabia?

If the situation is as described—renting a shop, furnishing it, and then either renting it out to another person for a known rent or operating it with someone for a known salary—there is no religious impediment to it, provided that the contract is based on one of these two options. This is because renting out shops is among the permissible transactions. It is not a condition for the lessor to own the shop itself; it is sufficient for them to own its usufruct (right to benefit from it).