The "awkward" stereotype does not describe most software engineers I've encountered in my career. Even "introverted" only applies to somewhat more than the average percentage in the rest of society, in my experience.
I don’t know where you work but I’ve worked with close to a dozen software teams and in all cases the vast majority of coders have been very awkward. The contrast with other fields I’ve worked in, such as business or finance is sharp.
Maybe it’s different in other countries but i doubt it, based on conferences I’ve attended.
I don’t know who you work with but I don’t find that true at all, so either we have a different definition of awkward or our companies select engineers differently.
Who could possibly feel welcome in an industry filled with awkward, mostly introverted geeks?