`$SHELL` still points to `/bin/sh` over SSH after `chsh -s $(which fish)`

I am using OpenBSD-current. After doas pkg_add fish, I ran chsh -s $(which fish) to change the default shell of my user qys to fish, and it works:

$ /usr/bin/ssh magicbane
Last login: Wed Aug 21 11:17:12 on ttyp0 from 100.94.151.103
OpenBSD 7.6-beta (GENERIC.MP) #270: Tue Aug 20 10:51:30 MDT 2024

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Welcome to fish, the friendly interactive shell
Type help for instructions on how to use fish
qys@magicbane ~> echo $SHELL
/usr/local/bin/fish

However,

$ /usr/bin/ssh magicbane 'echo $SHELL'
/bin/sh

I wonder why this didn't give me /usr/local/bin/fish? This is not a problem itself, but I suspect it has something to do with this issue that I'm trying to solve.