The size of the installer is 12,1 GB: do you have enough space to download the full installer?
Did the installer started automatically at the end of the download?
It should have started automatically if the file was downloaded completely.
Please note you need to run the installer instead following the standard update procedure from the Apple > System settings... > General > Software Update menu.
To run the installer open the Applications folder and look for the "Install Sonoma" icon: if you don't see the icon it means the download is not completed yet or you do not have enough space to download it. In such case delete some files (we all usually keep files in the downloads folder even when we don't need them anymore) and try to download the installer again.
Also, the full installation process takes at least 30/40 minutes to complete, so be patient.