The physical size of Pages 13.1 and 13.2 are the same — 441 MB. The physical size of MS Word 16.77.1 is 2.5 GB.
On my M2 Mac mini Pro w/ 32 GB RAM, running Sonoma 14.0, and no other user applications running, it takes Pages about 5 - 6 seconds to launch from the Dock, and about the same time to launch and open a 179-page Pages document. Word takes half the time to launch with or without that same 179-page document but as a .docx.
My Pages does not crash or freeze, so there is something else going on with your Mac. First, ensure that you have Pages v13.2 for Sonoma. Realize that on first boot, your Mac is checking software update, talking to the Mac App Store, launching up to 20 Spotlight worker bees, a Time Machine backup, and other housekeeping chores. This will slow your Mac for the first 15 minutes or so, and attempting to launch any application with this operating system activity will be more lethargic than at other times.
Next, if you have any anti-virus or so-called Mac cleaning documents installed, thoroughly remove them via the vendors instructions. Neither are needed and can cause collateral performance and damage, not only to applications, but operating system behavior.
When Pages has crashed, or hung, the very next use of it should be while holding the shift-key during Pages launch. This prevents it from loading its last saved execution state, and that can break a chain of misadventure.
I would also reboot your Mac in safe boot mode, if for no other reason than to scan your drive for errors, rebuild the font database, clear system caches, and other housekeeping. It will be a slower boot for these reasons, but also check if Pages launches without acrobatics. Reboot normally and see if Pages behavior improves.