They also don't give you a proper tracking number. The only way to track your shipment is in the app.

This is not correct. I do not have the app and get tracking for my orders.

I get email updates but whenever I click the track link it tells me I need the app.

I have a package on the way with AliExpress. It is headed from somewhere in China to somewhere in the US.

Using my computer just now, I looked at one of the emails that AliExpress sent about this order. It had a clickable tracking number displayed; I clicked it.

That brought me to their website, where I landed on a page that included the last update for my order and also a link to "View Details".

That works for me. It was very easy to where along the line my stuff is (and that it is not in the US yet).

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Meanwhile: I also copied the tracking number from the email. I pasted that tracking number into the box at usps.com.

The USPS knows of my tracking number and they do not have my item yet. Fair enough.

I ticked some boxes and told them to send me updates, which I'm sure they'll do once they have updates to send -- just as they have done for ~decades now.

This also works for me.

Many sites will work fine in a desktop browser but refuse to do anything in a mobile browser, demanding you install their app or just immediately redirecting you to the iOS or Android app store.

It does show a popup to that effect, but if you dismiss it you can still see the tracking info. Definitely annoying, but not unworkable.

If on mobile, ticking "desktop mode" in your browser usually goes around that dark pattern.

Depends on the shipping company, and likely on your location. I get tracking numbers for most but not all shipments

You just have to press the right link on the site and you get the tracking page (despite saying you need the app).