The installation of Xcode from the Mac App Store is quite slow and even without that dialog, would demand patience. It does require Sonoma 14.5 or later, which you have met. You can hover your mouse over that circular completion indicator to see its current activity and progress.
I would reboot your Mac, click on the Macintosh HD icon, and press option+cmd+i to open an Info panel. Look at the available storage number shown there. Xcode does not take just the storage equivalent of its download size, but considerably more storage as it is uncompressed and temporary storage during installation. That will increase should you choose more than the Mac SDK. Try the installation again later.