he told me I need to work on the clarity in the way I communicate with people
outside the team
Communication is about reaching understanding. It sounds like you (and some other responses) see this as an issue with your speaking, when most likely is has to do with your listening. As is the case with your post, it doesn't matter how clearly you speak, if you misunderstand the core issue, your words will not make sense. So start where you are likely to get the biggest gains - work on your listening.
And by "understand" I don't mean it's about intelligence. It's about simple things like, "I meant Brand X cookies, not Brand Y cookies." You think of them as the same thing and the other person didn't think of the options. That's what messes up communication, not realizing the other perspectives, options, etc.
First, spend more time listening. Listening is the biggest problem most people have when communicating. Notice that when someone important is in the room, people tend to listen more. There is an emphasis on listening in facilitate better communication and reduce misunderstanding. That is a clear indication that communication happens better when people listen.
Also, you notice other styles of communication, which gives you more communication options. You give others time to think about their responses, reducing miscommunication. Listening skills are hard to come by because very few people will say, "Shut up and listen more" (besides your parents..).
Second, practice reflective listening. This is where you spend your time trying to repeat what another person says in order to validate that you fully understood it. Many people think they understand what they hear and respond accordingly. If they didn't understand, things get complicated. This style of communication reduces those situations by proactively avoiding communication gaps. There is a lot to learn about how to do this, so read up on it and/or ask about it. Perhaps another approach will work for you better, but this is a good I see frequently used.
Third, read books on communication. There are many self-help books out there that are very helpful. I can post recommendations, but the core point here is that when you start down the path of, "I need to communicate better" you may hopefully realize that you can communicate better - and that's a good thing! Use audio books if you like. The idea here is to get a wide range of professional help - some of the topics you may need more help on than others. Books can cover a wide range of material that a site like this cannot really provide.
I suggest that you avoid asking for feedback from most people close to you, unless they have studied things like this and are capable of providing guidance. Some good communicators don't know how to coach good communication, just like some great athletes can't coach their sport. And some people that care and may want to offer help will not be helpful. A good example is probably your mentor - he doesn't sound like someone that could teach you to communicate well (and maybe you don't like his style) but based on your post, he got his point across. So maybe not the ideal coach for you.
After working on your listening skills, you should begin to gain speaking skills. Copying/mimicking those around you that are effective will be easy when you know how to listen to them for the information you want. If you decide that you want to be even more effective at speaking, there are books, references, etc. But, to emphasize, it doesn't matter how clearly you say something, if you don't understand what is being said to you, your polished speaking won't matter.