Android 13/14 - How to replace a system app with an older version?

I need to "downgrade" the google app with an older version because of a voice typing issue. However, the older version gets uninstalled after reboot. I have explicitly uninstall the original one then install the one I want, but after reboot, it's reverted back. I Know system app can be restored, thus an apk is probably resides in the system image partition. If I only disable/uninstall the google app, then it stays "gone" after reboot. So I need to disable the auto-update on system app if possible. Or replace the original with the older version in the corresponding partitions.