What DPI or resolution do AutoHDR output files have?

Your photos are full resolution — DPI isn't something AutoHDR controls or embeds as a setting during processing. Your AutoHDR photos have the full pixel resolution from your camera.

Why DPI doesn't affect quality

DPI (dots per inch) is just a metadata tag in the file. It doesn't affect pixel dimensions or image quality in any way. A photo that says "72 DPI" and one that says "300 DPI" are identical images if the pixel count is the same — the DPI number only matters when a printer or software uses it to calculate physical print size.

If you need 300 DPI for print

Set the DPI on export in Lightroom, Photoshop, or your delivery tool. It takes one click and doesn't change the actual image data. Your AutoHDR photos are print-ready as-is once you set the DPI tag on export.