Direct Routing has no carrier list. In Microsoft's words, you can use any PSTN operator. The connection is made through a session border controller, or SBC, a device that sits between the carrier's network and Teams. Microsoft supports only the SBC models it has certified.
Somebody has to make that connection work, and the planning page for Direct Routing lists what it involves. The SBC needs one or more carrier trunks. It needs a public IP address that Teams can reach. It also needs a fully qualified domain name under a domain verified in your Microsoft 365 tenant, with a public DNS entry and a trusted certificate for that name. The firewall has to allow Microsoft's signaling and media traffic. Then come voice routes, dial plans and the routing policies assigned to users.
Microsoft gives the reasons an organization takes that on. The planning page says Direct Routing fits organizations that have an existing carrier relationship, need to connect a third-party PBX or analog devices, need advanced call routing, want more control over their telephony, or run complex or multinational deployments.
Support follows the equipment. Microsoft's guidance for Direct Routing is to contact the SBC vendor when a problem occurs. The vendor investigates and escalates to Microsoft if needed. When a provider runs the SBC for you, your first call is to that provider under its support terms.