>"But steel-manning really helps break out of that pattern and meaningfully connect with what others are saying."
Steelmanning means that you ignore the argument your interlocuter makes, in favour of the argument you think they should have made. It runs diametrically counter to trying to 'meaningfully connect with what others are saying'.
If someone says 'X because Y', and you respond 'I think you mean X because Z but that's wrong', you have simply spoken past your interlocuter. Perhaps they actually meant 'X because Y2', but you didn't give them time to expand upon what '2' is. Or perhaps there's some other subtlety or depth that they have yet to expatiate.
There are lots of associated problems:
1. It is very difficult to say what a different version of the 'same' argument is. Perhaps you reason from different premises to the same conclusion. Perhaps you reason from the same premise to a better conclusion. Perhaps you use a similar style or tradition of argument. Really, only your interlocuter knows what 'their' argument is.
2. What you think is the strongest version of an argument is, may not be what a second or third person thinks the strongest argument is. In some realms - moral and political - there are no mind-independent facts in reference to which one argument can be objectively justified over another. 'Strongest' is therefore relative.
3. If you default to talking about an argument your opponent did not make, that is liable to create enormous confusion. If they did the same thing, you would end up never actually talking to one another. It would be like Chinese whispers, each rationally reconstructing the other's last statement.
What you really want to do is both 'interpret and understand' another's point of view, and then argue it through. The OP's link actually does a pretty good job of describing just that, but I think describing that as 'steelmannanning' is a misnomer. It's just philosophy as it has been understood for millennia. Steelmanning is supposed to be something more original.
Looking it up, this is claimed to be the original coinage of the word:
'Then we would be steelmanning, the art of addressing the best form of the other person’s argument, even if it’s not the one they presented.'[1]
[1] https://themerelyreal.wordpress.com/2012/12/07/steelmanning/