How sturdy is the USB-C port of the new M1 MacBook Air? What would be the approx repair cost if the port goes faulty?

First, part of the USB-C connector specification it self (Universal Serial Bus Type-C Cable and Connector Specification 2.0,

3.8.1.3 Durability or Insertion/Extraction Cycles (EIA 364-09)) states:

The durability rating shall be 10,000 cycles minimum for the USB Type-C connector family. The durability test shall be done at a rate of 500 ± 50 cycles per hour and no physical damage to any part of the connector and cable assembly shall occur.

Also, from what I could obtain from various teardowns of the new M1 MacBook Air, the USB-C connector assembly is connected to the logic board by a very short ribbon cable assembly.

Now, whether Apple will simply replace that assembly only if it is damaged remains to be seen.

Make sure to only use an original Apple charger and charging cable. Plus only use high quality accessories and peripherals from well respected brands to minimize the chance of damaging the Logic Board. Using poor quality USB-C devices with your Mac is one of the most common reasons for Logic Board failures along with liquid damage. Logic Board repairs are extremely expensive.

Only Apple or Apple Authorized Service Centre could answer your question. I suspect, because everything in Soldered to the LogicBoard or intergraded into the LogicBoard - it wold cost a lot

+1 :-))