Router in strange state, routes but can't log in via ssh

I have a router (MiktroTik hAP ac3, running OpenWrt 23.05.2) which at the moment is on another continent. It used to work fine, now it's in a strange state of partially working...

I can access it through a wireguard tunnel, and that works, as I can log in to luci using the wireguard tunnel. But after logging in, luci spins "Loading View" on the status page for about 30 seconds, and then gives me a partial page with "?" instead of the correct info in each field. Another 20 seconds later it gives me the Network section with the correct info for IPv4 upstream and IPv6 upstream, then nothing more (nothing for active connections).

Trying to log in with ssh hangs during host authentication... ssh -v gives the following...

...
debug1: kex: host key algorithm: ssh-ed25519
debug1: kex: server->client cipher: chacha20-poly1305@openssh.com MAC: <implicit> compression: none
debug1: kex: client->server cipher: chacha20-poly1305@openssh.com MAC: <implicit> compression: none
debug1: kex: curve25519-sha256 need=64 dh_need=64
debug1: kex: curve25519-sha256 need=64 dh_need=64
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY

...and then hangs until timeout.

Aside from the status page, some of luci's page work, others don't. The Network Interfaces page give an error " Error XHR request timed out" after about 20 seconds of "Loading view". I can reboot the box using luci's System -> Reboot, and it comes up back in the same state. The luci system log view works, but there's nothing interesting in the logs. Doing a sysupdate via luci doesn't work, it starts to upload the image but makes no progress.

Any ideas what might be going on? What else could I do to debug this remotely? Is there any way to get a shell from luci?

https://openwrt.org/docs/guide-user/troubleshooting/failsafe_and_factory_reset#entering_failsafe_mode

Then:
mount_root
sysupgrade -b /tmp/backup.tgz
download that file
upload image from firmware selector to /tmp/ and upgrade to same or later version without preserving config.
You can restore config in fresh install, if it breaks again, go back to failsafe, reset with firstboot ; reboot
Then you need to unpack backup file and more or less re-type all parameters found in there one by one.

Thanks, but that won't help me because the only way I have of interacting with the router at the moment is over the Internet through a wireguard tunnel.

Deeplink to firmware operations for backup and sysupgrade:
https://openwrt.lan/cgi-bin/luci/admin/system/flash
Otherwise no chance if none of remote admin functions work.