Delays with the supply of parts is an ongoing issue affecting the industry on a broad scale, so unfortunately your experience is not uncommon. Also the availability of parts can vary considerably depending on the part required, where it is coming from and the manufacturer, so there isn't really a single answer to how long it is reasonable to wait. We would hope that the dealer or garage is making every effort to get the parts for you as soon as possible.

Ordinarily we would suggest asking the garage if they would be happy to fit parts you supply yourself, but as this work is being carried out under warranty this is unlikely and would mean extra expense for you. Unless you are prepared to accept the cost yourself, unfortunately your only option is to firmly but politely keep the pressure on the garage to obtain the parts and complete the work.