The definition of a Drivetrain is all of the components connecting the motor to the wheels(including axels). Powertrain is the drivetrain plus the motor. Tesla does not have a "drivetrain" warranty like BMW. Tesla has a "Drive Unit" warranty.
The "drive unit" itself which contains the motor, inverter & gearbox is covered. I recall the mechanics stating the P85 drive unit was a $150 remanufactured part, after subtracting the core cost of the original. If you really do need axels, then those prices look accurate(assuming they don't give core recovery prices). If that Tesla service isn't sure the parts will fix it, find a different service center. Choose one of the older centers that's been around since 2013 if possible. Make sure they completed all of the service bulletins on your car. If they skipped a related bulletin that was at the discretion of the inspecting mechanic during your 4 year period, you can argue that they should have done that bulletin. If it came out during your ESA period, they should still do it for free now, since they opted not to earlier.
I originally bought a demo P85 in 2013 (no miles, just a mall show car). When I had a clunking noise, they replaced only the drive unit and added the bulletins updated washers and wire ties. Then when that reman unit started rumbling they replaced it again, more bulletins, didn't have any issues after that. I've never heard of a base S60 having the same issue, it was always the P85's (and roadsters) that were in the local shop for repairs.
Honestly, the noise won't leave you stranded for a long time. if it's not noticeable just keep it another 10 years. I'm actually surprised the service center didn't pre-empt the conversation by giving you the trade-in offer. You may not want to consider it at all, or maybe you do. Sell Tesla the S 60, and they will send you off in a new or pre-owned 75D. Tesla sales probably won't count the repair against the trade in value, since the new owner gets a fresh warranty anyway. Not sure your car specs, but trade in might be around $35-40k usd. Since they sell 2013 S60's ~ $40-54k usd. A newer 75 has better range, 4th gen powertrain platform, AP, would leave you with a payment though. Tesla has "demo" cars which qualify for the federal US tax break, where as the "Pre-owned" cars do not. Doesn't NJ give a sales tax break on new Electric cars?