Does rotating a PDF reduce its quality?

No. Rotation only rewrites the page's orientation flag; the text and images inside the page are copied across byte-for-byte. The output is the same quality as the input.

Why does my scan open sideways on the portal but look fine on my phone?

Phone galleries often apply the orientation stored in the file's metadata while portals ignore it. Rotating the pages here writes the correct orientation into the PDF itself, so every viewer shows it the same way.