Why PNG suits pages with text and lines
PNG stores exactly the pixels that were drawn, with no blocky noise. Edges of letters, thin lines and flat areas of colour come out as sharp as the resolution allows, and you can open and save the file again without losing anything. That makes PNG the format for slides, diagrams, forms and screenshots of documents, and for pages you will place in another document or edit in an image program.
The pictures are 8 bit colour, drawn with the same smooth edges (anti-aliasing) a PDF reader uses on screen. At 150 DPI an A4 page is 1240 by 1754 pixels, and at 300 DPI it is 2480 by 3508 pixels, with four times as many.
Transparent background: what you get
Normally a page is drawn on a white sheet. With Transparent, it is drawn on a clear one, and only what the PDF paints appears. Whether that leaves clear areas depends on how the PDF was made. A PDF that paints no background gives you its text and shapes on a clear surface, ready to place over a coloured slide or a web page. A logo that was exported as a PDF is a typical example. When you convert a single page, it is shown on a chequered background so you can see which parts are clear.
A PDF that fills the page with a colour, or draws a white box behind its content, keeps that colour, because the PDF really paints it. Slides with a background are an example. A scanned page is a picture that covers the page and has no clear parts either.
Soft edges are partly transparent, which is right on a light background and can look thin on a dark one: black text on a transparent page may be hard to see on black. JPG cannot be transparent, so the choice is off in PDF to JPG. WebP can be, and is offered in PDF to Image.
Smaller PNG files, and why they are still large
PNG compresses without loss, so its size depends on how regular the picture is. A page of black text on white shrinks well. A page with a photograph, or a scan, does not, because the grain and noise of a photo cannot be packed without losing something. At 300 DPI an A4 page has 8.7 million pixels, so a page that holds a photo can be several megabytes as a PNG.
Make PNG files smaller runs an optimiser that finds a better way to pack the same pixels. It changes nothing in the picture. Text pages often get several times smaller, but each page takes longer to save, and the panel gives an estimate when a job will take 20 seconds or more. Switch it off for a quick result. For pages that are mostly photographs, PDF to JPG makes far smaller files.
The pages are drawn one at a time and released before the next. The finished pictures add up in your browser until you download them, so the tool warns before a job that is likely to be very large. A page above the size limit of the browser, about 67 million pixels on a computer and 16.7 million on a phone, is drawn at a lower resolution, and the result says which page and how much lower.