The last version of Pages (v13.1) came out three months ago. It will only open undamaged .pages, .doc, .docx, .rtf, .rtfd, and .txt files, regardless of platform. It may not open some Word documents depending on their age, or if they are damaged, and rarely, even MS Word will fail to open some Word documents too.
Why Pages makes a copy of a document when you open it may be pilot error as that does not happen for me when using Pages on iOS, iPadOS, or macOS.
See: Pages User Guide for iPhone - Apple Support
No other word processing application will open your Pages documents except Pages, so abandoning Pages before exporting each document to Word .docx (may not be accurate conversion) would leave you with unusable documents. If you export to PDF, then MS Word v16.31 or later will convert the PDF into .docx.