Wider tyres are more comfortable and - as is broadly accepted now - don’t hamper rolling resistance too much, actually being faster in some circumstances.
32c tyres are fine for bikepacking on mainly roads, but if you are going to be mixing roads and gravel, 38c makes a better option. If you’re going mainly off-road 700 x 45c - or even as far as a 650b x 2.1 inch MTB tyre - will provide better comfort and control.
Tread pattern is also an important consideration. If you are going to be ridding in deep loam or sloppy mud, you’ll need a tyre with knobs to dig in and provide some mechanical grip. On the road, tread pattern is less important, with the size of the contact patch being the greatest determinant of grip. For mixing road and gravel, a semi slick will be the best option, providing low rolling resistance in the centre of the tyre, but with knobs that will dig in when cornering on soft surfaces.