I have an old EA6350 v3.
I've just completed the following quick tests.
I had been booting 22.03.5 off one partition and OEM fw was resident on the other partition.
I installed 22.03.6 sysupgrade.bin overwriting OEM fw.
Adjusted the kernsize boot variable, and rebooted.
I installed 23.05.2 factory.bin keeping no Settings. Router booted fine. Speed test ok via ethernet.
I then cycled power switch 3 times to revert back to booting from 22.03.6.
I installed 23.05.2 sysupgrade.bin keeping no Settings. Router booted fine. Speed test ok via ethernet.
I then flashed latest OEM fw using LuCI. Router booted into Linksys GUI.
Flashed OEM firmware again from the GUI.
Installed 22.03.5 factory.bin.
Changed the kernsize boot variable back to original value, and restored my old settings.
Cycled the power switch 3 times.
Router booted up Linksys OEM fw. Installed 22.03.6 factory.bin
Changed the kernsize boot variable.
Upgraded from 22.03.6 to 23.05.2 using sysupgrade.bin overwriting OEM fw, keeping No Settings. Router booted fine. Speed test ok via ethernet.
Conclusion
It would appear both 23.05.2 factory.bin and sysupgrade.bin seem to work when upgrading from 22.03.6 for EA6350 v3.
fwiw, I've inspected the revision history MR8300, EA8300 and EA6350 v3 device pages. As far as I can tell, the MR8300 was first device page out of these three, to include instructions for installing 23.05 using factory.bin. I think it was edited by @badulesia in May 2023 ? The EA8300 followed in August 2023 and EA6350 v3 in December 2023 by different authors who may have used MR8300 device page as source.
There may be a lost explanation for why 23.05 factory.bin had to be specifically used in the past, perhaps related to snapshots at the time?
Update: Later forum post and LuCI sysupgrade message stipulating use of factory.bin