This is not a port of xbindkeys, but I think it provides similar functionality. Sadly the sway wiki does not really mention it but it is in the
man 5 sway
Switches to the specified mode. The default mode is default.
mode [--pango_markup] <mode> <mode-subcommands...>
The only valid mode-subcommands... are bindsym, bindcode, bindswitch, and set. If --pango_markup is
given, then mode will be interpreted as pango markup.
it is also mentioned in the Arch Linux wiki Control swaynag with the keyboard and in at least one issue 'mode --pango_markup' compatibility).
I believe it works the same way that the i3 config does. I will be testing it soon. The i3 manual Binding modes section looks like the best source for learning to use this feature