I found the answer to my question from this post about another Extreme Networks product.
The answer: user/password are admin/new2day -- on my AP3825i, this applied both to the bootloader and to the Busybox shell once the onboard Linux had booted.
Update: I completely missed this PR which should support the board already.
Update2: The above is the OP of this thread having difficulty spinning up a port.
Update3:
You have made a mistake here: the flash is 0x4000000 (64MiB) long, not 0x2000000 long.
Update4: I haven't been able to make much progress: I am stuck at the same place as OP. I have pushed my code here: https://github.com/hurricos/openwrt/tree/ap3825i
Update5: I have publicly requested a GPL modification dump from Extreme Networks here: https://community.extremenetworks.com/extremewireless-identifi-233215/acquiring-a-gplv2-dump-of-linux-kernel-modifications-for-the-ap3825i-7831344
Update6: There is a known issue with booting Linux on PPC built using GCC10. This was avoided in all of my builds (which were on top of GCC11 / master, or, more recently, GCC8 / openwrt-21.02).
Update7: Still no dice. @blocktrron suggested that the onboard U-boot image may be manipulating my device tree; it might be possible to replace the U-boot copy, but it sounds daunting.