In WordPad, File, New means start a new document, not a new page. To continue with your current document, you would just keep typing. But, as others pointed out, WordPad provides no option to create a page break, so it's too limited for your purpose. Using the free, online version of Word or the free Google Docs program (or many other programs) will work much better.
Transferring your WordPad document to Google Docs, with all formatting retained, is a simple matter of starting a new document in Google Docs and then using File, Open, Upload.
Ironically, I was not able to find a simple method to transfer (with formatting) from WordPad to the free online version of Word. Since Word has existed for decades as a full, locally installed application, searching for instructions lands you on instructions for those versions instead of the online version. I'm sure there must be a method. I'll update this post if I learn more.