Why Word documents opened and saved in Pages have larger file sizes?

Word documents are neither 32-bit nor 64-bit and yes, the current versions of Word will open older Word documents from years ago. The current Microsoft applications are 64-bit as required by macOS Catalina through Monterey and beyond.

Because Pages is not a Word clone, and when you open a Word document in Pages, it is translated into the internal Pages .pages document format — without changing the original Word document — and is a different, larger document format by design. And there is another translation process on export back to Word document format. Apple does not guarantee these translations to be accurate, or produce smaller documents as a result.

If you want to open/edit/save Word documents in their native document format on Mac, then you need a currently supported version of MS Office on your Mac for that purpose.

Microsoft also offers the single-purchase Office 2021 for Mac option. I managed to purchase Office 2021 Home and Business for $50USD. Some bargain sites may still have that offer available on the web. It requires macOS Catalina or later for installation (at this time) and I have it installed on macOS 12.4.