When we had Macs sent out for repair by my employer:
- Logging the service request with Apple took several days to work through its queue.
- It took a day to pack and get ready to ship.
- Shipping could take several days.
- Apple receiving could take a few days to log and enter into their local service system.
- The actual service usually takes an hour or two, but if complications are encountered, could take a day or more.
- Then it needs to be tested, and sent to shipping for return.
- It may take a few days to get packed and shipped.
- Shipping can take several days.
- Receiving that package can take a few days depending on backlog. It must be logged and routed for return to customer.
If you add all this up and factor in weekends or holidays, this can amount to easily 3-4 weeks.
If shipping goes overseas, it can take a lot longer.
Currently, there are parts shortages and that can add time too.
I have had good experience with repairs being done at a local Apple Authorized Service Provider. They do repairs right there in the shop and I was allowed to speak directly with the technician doing the work. It also eliminated all the delays associated with packing and shipping as the work was done locally.
I doubt your Mac is lost as everything is tracked with bar codes.