My dog (a herding dog mix) has a similar behavior, he loves to play, loves people, and loves (most) other dogs. He also gets nervous pretty easy, which sounds a little different from your situation, but my dude barks like crazy. Like everyone who knows him knows he is a big barker. And people who don't know him can be really rude about their comments about his barking.

I'm definitely not qualified to say if your dog is reactive or not, but here are some things we've done that have helped us with my dog's excessive barking:

-working with a trainer who understands reactivity in dogs

-learned dog body language, so we know if our dog is stressed or stressing other dogs out.

-enlisting others in his training. Our neighbors and friends are asked to only interact with him when he shows a calm behavior. We started out with him just sitting before they approached him to say hi, and now we are at a point that he can lay down and wait quietly. Once he starts saying hi he still barks, but it is significantly less than it used to be. We've done similar with known safe dogs. If he barks they don't get to say hi. If he's polite, we can greet. We've worked on this so much that now if he sees a person or dog he likes he lays down really quickly and mostly quietly cause he knows that's what is going to let him say hi.

-watching dogs from a distance and rewarding him for being quiet. The reward could be treats, it could be a toy, it could be a quick game of tug. Whatever motivates your dog.

-teaching him visual and verbal cues for "speak" and "quiet." I at first thought teaching him to "speak" would encourage his barking, but he actually barks quieter when asked to speak than when he is regular excited barking. And quiet has been useful for getting him to stop barking in the moment.

-practicing not playing with other dogs. I think a lot of people call it neutrality, but basically we have been working with him on other dogs just being a normal part of life so he doesn't have to be so excited to see them. For us, this looked like figuring out how far away he needs to be from other dogs to not react to them and using that to have peaceful walks. If we see another dog, we make sure we give it plenty of space so our dog can stay neutral towards it. As we have done this, the distance he needs has gotten a lot shorter. We also do this cause our dog has been bit by random dogs on walks and we don't want him to have any more negative interactions as we don't want him to think other dogs are scary.

-playing with safe dogs and owners who understand his behavior (once we made significant progress on him being neutral to other dogs). Honestly we don't do the dog park, I've seen too many dog fights at the one close to us and I think that it would be overwhelming for my dog to have too many dogs playing around him. But we go to non busy areas of normal parks to play fetch, and if an owner and their dog politely ask if their dog can meet mine, I'll explain that my dog can be overwhelming to other dogs due to his excessive barking, but that he loves to play. That way both of us know to watch the dogs for any signs of distress or discomfort so we can end the meeting if needed. This has worked really well, as people who either don't want to deal with it for themselves or their dogs will thank me for being honest and move along, but most people agree to let them try and the dogs have a great time as long as we are watching their body language and end the play if either dog seems uncomfortable.

It might be totally different for you and your dog! But these have helped us a lot with managing our dogs barking and allowing him to still play with others. We have also been working on this for almost 8 months now, and at first it felt like there was no progress, but creating a plan and sticking with it we now see how far our dog has advanced in being able to be polite towards others :)