In the US, Apple has gotten really fast with turn around times on mail-in repairs (years ago it would always take a week, but we've received some back in 3 or 4 days), but I agree with @leroydouglas, that a mail-in repair can still take 10 days. It all depends on weather across the country & the shipping carrier's ability to ship on time. Sometimes another part may be needed, or another issue is detected which may take time for the technician to troubleshoot. I can tell you from personal experience supporting my organization's Macs, that it can be very hard to troubleshoot some failures these days.
Having said that, whoever mailed the laptop into an Apple mail-in repair depot should be able to create an escalation to check on the status. The tech should be able to at least verify the mail-in repair depot received the laptop & may even see some activity from the tech at the mail-in repair depot within their service portal.
No one should ever guarantee a turn around time for any repair since there are so many ways the repair could be delayed. It is one thing for a tech to mention that typically they get mail-in repairs back within X days, but there are always exceptions where delays may be encountered so no guarantee should ever be given. Even if the repair shop was doing the work themselves, the same thing applies since things happen that can make a particular repair take longer than expected.
If the suggestions & links provided by @leroydouglas don't help, then you can try contacting Apple corporate to voice your displeasure at not being able to get a status update on the repair. Keep in mind any complaints Apple receives about an AASP will most likely be investigated with Apple contacting the AASP to get their side of the story as well.
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