In both of those, the barking looks like her attempt to initiate play. It doesn't look particularly nervous, but it's not exactly graceful dog communication, so it's not working that well for her. The corgi in the first video, for example, found it annoying and told her so.
I don't see as much insecurity as I expected, but she certainly isn't a very confident communicator either.
I think these situations might be a little out of her social abilities for now. Anything that's creating barking jags is probably a situation you should try to avoid until her confidence is higher. A couple of barks here and there are fine, but any time you see her bleeding off all her excess stress by barking, it's probably a situation that's going to make the problem worse, rather than better, since repetition of a habit helps ingrain the habit.
I think this is spot on and really good advice. Do you have other opportunities to work off some of her extra energy and then work on her socializing instead of the dog park? I would worry about her behavior getting her in trouble with a dog that didn't handle it as well as the corgi did.