Instead of involving a third application (e.g. TextEdit), why not perform a simple copy/paste into a Pages Text box after you have clicked on its Type to enter text placeholder. That will perform the table to text conversion, which you can leave in a repositioned, rescaled text box, or copy the tabular text from the Text box into your body text and remove the Text box.
To go from tabular text back to table, you can insert a new Pages table, copy the tabular text, and then by single-clicking the first cell of the Pages table, you perform a simple paste. You can also do this back in Numbers by single-clicking the recipient cell and performing a simple paste from the selected Pages tabular text.
This isn't theory, but what I used for years in Pages and Numbers, including the current v15.1.1 (Pages) and v15.1 (Numbers).
It is long since overdue for the Pages product team to introduce a practical menu item for two-way table and text conversion. It was last present in Pages '09 v4.3, but current in LibreOffice 25 and 26 builds, and even Word 16.106.1 has a simple Table menu item to perform two-way conversion.