erase-install.sh can only work with full installers. In fact, the only way to update using "update files" is using Software Update.
Doing it that way will always grab the full installer. If you want to grab the stub installer you need to use the MDM commands. Apple has been very clear, if you are using CLI to handle OS updates, stop.

Below is what we use. Change the "Ventura" to whatever OS you're trying to patch.
#!/bin/bash
todayDate=$(date "+%d.%m.%Y")
patchingLogFile=patching_"$todayDate"
exec > /tmp/"$patchingLogFile".txt 2>&1
echo "Part 1:0 log file has been created"
getosupd=$(softwareupdate -l | grep "Ventura" | awk NR==1 | cut -d ' ' -f 3-)
softwareupdate -i "$getosupd" -R 2>&1
Doing it that way will always grab the full installer. If you want to grab the stub installer you need to use the MDM commands. Apple has been very clear, if you are using CLI to handle OS updates, stop.

For clarification: stub installers are not the same as the updates that you obtain via the softwareupdate command, the Software Update pane, or by using MDM installASAP commands.
Stub installers are not really very useful. They are smaller but only because the payload is downloaded upon running it. If you use startosinstall on a stub installer it takes far longer than the combined time of downloading the full installer and running it. I'm not even sure Apple are providing stub installers any more.
erase-install was never intended to be a utility for performing incremental software updates, but has become popular for doing this due to the unreliability of the softwareupdate command and poor options for MDM software update management. If we are lucky, Apple will fix those issues and render erase-install unnecessary :)
@grahamrpugh is correct IMO. The mass action update commands are not reliable on macOS 13.
I think Erase Install is the most reliable way to update standard users from 13.0 to 13.2.1 right now.
I email folks asking them to update right before they go to bed so the long process can happen while they sleep.
This is a link to a film of my workflow with Nudge and Erase Install.
Hope that helps! ~ B