If you are initiating the installer from within macOS, then most likely you have some third party software installed which is interfering with the normal operation of macOS. Try booting into Safe Mode and initiate the installer. If the problem is with the second phase of the install process, then boot into Safe Mode again for phase 2.
Otherwise you can try installing macOS Ventura from Internet Recovery Mode (Command + Option + R)....however, some Macs may instead boot into the installer for the OS which originally shipped with the Mac from the factory.
If you have modified the security settings for the laptop by using the Startup Security Utility to allow booting from USB drives, then you can try using a bootable macOS USB installer instead.
FYI, both Internet Recovery Mode or a USB installer will require a lot more free space on the boot drive....something like 50GB free.
In extreme cases where none of these methods work to install macOS, then you may need to "Restore" the firmware to reset the T2 security chip which will also destroy all data on the internal SSD. Afterwards you will need to use Internet Recovery Mode to reinstall macOS as a USB installer will not work since you will not be able to authenticate to allow booting from USB due to the reset.
If you don't already have a good backup, then I highly recommend you make one now before doing anything else. There are a lot of ways to permanently lose access to your data on the 2018+ Macs.