Do carbon taxes in place today apply to carbon embedded in imports? I’m giving the example of Sweden whose carbon tax is highly regarded and which is the highest in Europe. 
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Sweden has a carbon tax of €110 / t. Source

This tax does not apply to installations covered by the EU ETS. The EU ETS applies to 45% of all carbon emitted in the EU and currently only prices carbon at around €25 / t. 
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Moreover some 45% of primary energy consumed in Sweden is nuclear and hydro making Sweden’s energy supply relatively less dependent on carbon emissions. 
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As a consequence of the carbon tax and the high share of non-fossil energy generation Sweden’s per capita carbon emissions are low by international standards (5.5 t CO2e / capita / year). 
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However, when measured by consumption Sweden’s per capita emissions are relatively high (15.4 t CO2e / capita / year). 58% of carbon consumed in Sweden is imported. 
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This makes me think that there could be tendency for expensive domestic carbon emissions, especially those not covered by the cheaper EU ETS, to be substituted with carbon embedded in imports – unless the carbon tax would apply to imports as well.
I think the answer is generally/overwhelmingly "no" there usually not a embedded carbon (import) tax in most jurisdictions. A 2019 paper says:


  The idea of a BCA is not new. In the US, for example, lawmakers have tabled several proposals to introduce a carbon tax. So far, though, no country in the world has an operational BCA. 


Supposedly the EU Green Deal was supposed to include one, but I haven't followed the developments. (There have been arguments against it already. And the US has already threatened to retaliate should the EU adopt it.)