If choosing Paste or Paste And Match Style do not avoid the text in a Text box issue, then you will need to select the text in the text box, copy it to the clipboard, click in the body text of your document, and paste. Then you can remove the Text box. Or, first paste into TextEdit (Rich Text format), and then copy/paste that content into Pages.
There are no changes you can make to Pages to avoid this pasted content into a Text box issue as it has to do with application design and how it interprets content from the clipboard.
This morning, I visited several different websites where I selected and copied/pasted that text content into Pages v14.3 without any occurrence of a Text box. Some text, when just pasted from The Brave browser did not have the proper text encoding and only boxes appeared. Undoing that, I chose Paste And Match Style which resolved the text encoding issue. Under no circumstances did the pasted text result in a Text box. One can select text on a website, click, hold, and then drag the text-clipping into Pages, also without a resultant Text box.
This does not mean that some webpage text does not result in a Pages Text box, because that happened to me yesterday, though I don't remember the website or the context of that copied material. The next time this happens, I will look at the website coding and inspect what that browser put on the clipboard in more detail.