This bug can be closed. The issue occurred on my system due to misconfiguration of macOS’s newsyslogd.
By default, newsyslogd inserts a timestamp into a file after the log has been rotated - the new file receives the timestamp. Since emacs expects savehist files to be formatted correctly as elisp, this leads to the error I saw on startup.
The fix for this is to modify the newsyslogd command to use the “B” flag. For example:
# logfilename [owner:group] mode count size when flags [/pid_file] [sig_num]
/Users/username/.emacs.d/.cache/savehist username: 644 5 * $W0 JB