The backpack examiner oddly doesn't do that.
Is there any other site which offers that service, or maybe even an in-game interface I have somehow missed?
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Use tf2ls and choose the "Extras" option, or "Text Output" for text instead of icons.
You could use TF2Toolbox and set it to Plaintext and look for 'x2' and 'x3', etc.
Actually, tf2items.com does offer this. Go to tf2items.com and enter you profile ID. (If you don't have a profile ID set up, just copy the link to your community page)
On your backpack page it will show 3 different tabs, the last one - checklist - should be exactly what you need.