Can I measure inductor current by adding a secondary winding?
For the AC component you can use a simple current transformer. You can directly wrap a
few loops of wire around the current carrying wire (i.e. use air as the core material) to test the concept, or you can buy a pre-existing solution.

However, a buck converter will have some AC+DC component, and any transformer setup cannot measure the DC level.

There are only 2 solutions for measuring the DC level: hall effect sensors and current shunts. I don't understand why you think a hall effect sensor will necessarily be expensive (possibly a locality issue?): take for example the DRV5053RAQDBZR, which digikey sells for about a dollar in 1-off quantities.

As PlasmaHH meantioned, there are current shunts available which can measure these currents with ~100mV or lower burden voltage, however they are usually somewhat expensive. If you don't need to worry too much about tempco, you can just use a length of wire with a known resistance (measured before-hand using 4 terminal sensing).