The size must be correct in the original app BEFORE you make the PDF. In Photoshop make sure it is a4 (210 x 297mm exactly)
Your sizes in the second screen shot are larger than A4.
Open a new document from the Print tab and choose A4 and make sure that the resolution is 300dpi
Either group all your layers in the original, ao make them a Smart Object, and right click and Duplicate them to your A4 template.
Free Transform them to fit the new template, and save as to PDF using the High Quality Print preset.
Leave all type and vector layers as they are (don't flatten or merge layers).
When you have saved the PDF open it in an app like Acrobat and zoom way in to make sure it stays sharp.