Running the test is simple but getting good primers nowadays is easy because they can be bought and arrive 24 hours later. If the sequence is published, then even the lab manager can get them.
Yes, labs don't synthesize their own primers. They buy them from suppliers. The kind of primers you would use for SARs-Cov2 would be about $10-$20AUD (similar for USD) a vial and be sufficient for several hundred reactions (maybe a hundred or so tests with triplicate replicates, pos and negative controls). The thermocycler and the technician doing the pipetting are the expensive bits, not the primers!