I am not sure I understand these points. There is no longer a lounge category by default. But when it existed, the default security settings were viewing and posting for TL3 and up. So TL3s were included in the lounge. You can still create such a category, and if you have an existing lounge category, you can also change who is able to access it.
Which moderation functionality do you mean? Most permissions are controlled by site settings. So if you don’t want users with TL3 to edit topics (improve titles, tag, recategorize), then you can remove that group from the edit_all_topics site setting.
I wouldn’t phrase it that the software decides who you can trust. For me, trust levels are an automated system granting the user more permissions after showing a certain interest in the forum. The trust they earn is about them not abusing the permissions they receive—for example, to post spam.
I like the image Jono Bacon used in his YouTube video about Discourse trust levels: Think of a new member in your community like someone ringing at your door. You don’t know that person yet, so you don’t know whether they want to become your friend or sell something to you. So before letting them further into your house, you want to get to know them better. In the same way, you don’t know whether a new member of your community is a spammer, a troll, or a good person. That’s why it makes sense to limit the permissions of what new members are allowed to do. And with more than a few users, you need an automated process to remove those limitations.
Also, I feel like your posts might deserve their own topic because they seem to be about trust level 3 in general, not about showing the progress to users.