23.05.0 is already running with DSA. Anyway, this target (mt7621) has moved a long time ago to DSA. Your issue is not related to DSA.
You are attempting to flash on partition 2 from partition 1. The bootloader fails to boot OpenWrt on partition 2, and than fallback on partition 1 where is the previous 23.05.0. This is the expected behavior. Install luci-app-advanced-reboot to check partition contents.
Please read again the previous message, it's the only way to upgrade this device. I'm using it for a couple of years now.
You don't have to rebuild from scratch: save the settings, return the Linksys OEM, flash the newer factory image, restore the settings. This is what I'm doing for each upgrade. It works just fine.
Last but not least: wait a few days, 23.05.5 is coming soon. But you may also want to experiment upgrading with 23.05.4 before.
EDIT : it pops out of my mind that you may have busted Linksys OEM on partition 2 by attempting to flash OpenWrt on it. It is mandatory to keep Linksys on partition 2. Check the content with luci-app-advanced-reboot. I would recommand to return to a safe config by using TFTP to install Linksys OEM to both partitions. You may have to use a serial link for this. Than flash OpenWrt on partition 1.