This basically confirms my experiences, the way I improved my social anxiety and public speaking was with (forced) immersion therapy from the public speaking and communication I had to do in college, and at work to a lesser degree.
It would be nice if Software Engineering jobs would involve more human interaction. With all this Scrum I have the impression the Engineer is supposed to only work on tickets, have no meetings ideally because it's more efficient when Product people etc. do that.
Many flavors of Scrum have daily standups where you must (briefly) talk to the rest of the team, and also involve doing pair programming where you are constantly discussing something with another team member sitting next to you. (This last part actually saps my energy and is something I don't enjoy about agile methodologies...)
The problem is that highly technical and focused conversation seems nothing like aimless conversation in social situations.
I also think that for most mundane tasks pair programming is more of a burden than an improvement. For really difficult tasks that take hours to just imagine the solution, it can be actually productive to sit together and solve it that way.