Where exactly does the tracking number go?

On the order page, in the tracking field above the comments box. Entered there, it becomes a link your buyer can click from the order.

Is filling it in compulsory?

No. It is an optional field, which is the root of most of this: buyers cannot tell the difference between a seller who left it empty and one who filled it in somewhere they are not looking.

Should I mark the order shipped before it is at the post office?

Sellers disagree about this, honestly and at length. The practical risk is the one above: a status set at label time gives your buyer a number that returns nothing for a day or two, and an early scare costs you more messages than waiting would have.

My buyer keeps asking even though I filled it in. What now?

Send them the number, in a message, with the carrier's name and a sentence about when it will start moving. Arguing that the information was already available is correct and does not help — they are asking because it did not reach them.

Is there a way for the buyer to just have it?

Only if you put it somewhere they were already going to look. That means sending it rather than filing it: a message, or a link of your own that carries the tracking with everything else about the parcel.

You filled it in.
They still can't see it.

The tracking number almost always exists. What is missing is the short distance between where you put it and where your buyer is looking.

Where it gets lost

It is on the order page, and they are reading their email

The tracking field lives on the order page, just above the comments box. A buyer who is waiting for a message will not find it there, and has no particular reason to think of going back to an order they have already paid for.
You entered it in the message thread, not the field

Both are on the same screen and both look like the right place. Only the field turns into a link on the order page; a number typed into a message is a number in a message.
The carrier has not scanned it yet

A number issued when the label is printed returns nothing until the parcel is physically taken in. Your buyer clicks, sees no such consignment, and concludes the number is wrong. It isn't — it is early.
The number is real but not theirs to follow

Some domestic services return results only to the sender, and some cross-border ones stop reporting at the handover and resume under a different number in the destination country.

Filing it is not the same as sending it

Everything above has one shape. You put the number in the right place, and the right place is somewhere your buyer has to decide to go. A paid order is finished business from their side; they are watching their inbox, not an order page.

This is why sellers end up answering the same message on every sale, and why the number of times you are asked has almost nothing to do with whether you filled the field in. It is a distribution problem wearing the costume of a data-entry problem.

The fix, whatever you use to do it, is to make the information travel: something that arrives, on the day you post the parcel, carrying the carrier's name, the number, and enough context that your buyer does not have to work out what they are looking at.

And say when it will start working

One sentence prevents most of the follow-up: say the number will return nothing until the carrier takes the parcel in. Buyers who click straight away and see an empty result do not conclude that it is early — they conclude that it is wrong, and the next message is about that instead.

Where Sillon fits

Sillon is a €9-a-month tool for Discogs sellers that turns each dispatch into a link you send. The page behind it lists the records on their way, the carrier, the tracking number as something clickable, and the photos of the parcel. It opens with no account and no app, and it is a thing your buyer receives rather than a field they have to go and find.

A message with the number and the carrier's name does most of this for nothing. The difference is that you would be writing it by hand on every sale, which is exactly the point at which people stop doing it.

See what Sillon does See what your buyer gets

Questions

Where exactly does the tracking number go?: On the order page, in the tracking field above the comments box. Entered there, it becomes a link your buyer can click from the order.
Is filling it in compulsory?: No. It is an optional field, which is the root of most of this: buyers cannot tell the difference between a seller who left it empty and one who filled it in somewhere they are not looking.
Should I mark the order shipped before it is at the post office?: Sellers disagree about this, honestly and at length. The practical risk is the one above: a status set at label time gives your buyer a number that returns nothing for a day or two, and an early scare costs you more messages than waiting would have.
My buyer keeps asking even though I filled it in. What now?: Send them the number, in a message, with the carrier's name and a sentence about when it will start moving. Arguing that the information was already available is correct and does not help — they are asking because it did not reach them.
Is there a way for the buyer to just have it?: Only if you put it somewhere they were already going to look. That means sending it rather than filing it: a message, or a link of your own that carries the tracking with everything else about the parcel.