Unlike Pages (which is no Word clone), MS Word has had over three decades of evolution in supporting large corporate documents, and may actually load the document in RAM, in addition to internal coding that can handle large documents.
Pages was never designed to be a corporate word processing application and its glass jaw is just that, it doesn't do large documents well, even if on the start-up drive, on a high-performance Mac with plenty of RAM. Users have been complaining about this since Oct 2013. I have opened Pages documents on iCloud Drive and observed that autosave takes longer to update the document content specifically owing to the network traversal delays.
Since you have access to Word, and it behaves as you expect, my recommendation is to use Word, where you open, edit, and save documents in their native document format. Something that Pages also does not do (with opened Word documents).
There will certainly be a typing lag for the first few minutes on startup as there are several System processes also running (Spotlight, SoftwareUpdate, etc.) that would compete with Pages for CPU cycles.
