Ok, before I say what I am going to say, please know I mean this in a good way, even if it may sound a little different. (Just making sure you know that)

I am one of those people who believe that for the most part we have control over our feelings. Even the irrational feelings.
Dr. Michael Edelstein says that "..we enter into every situation with certain beliefs or expectations. Those beliefs and expectations directly influence the way we are going to end up feeling about the event or person."
If you enter the situation with your mentor with these fears you already have, your mind is already shut down to any other belief. You are already jealous, you are already anxious, you are already afraid. And you haven't even met the person yet.
So then you enter the situation and you already feel trapped in your issues and they will become a problem because in your head you already think of all the situations that might make you jealous or feel abandoned or neglected etc. The fear of that happening is understandable. But you are creating a reality for yourself that will probably happen because your beliefs and your mindset is already made up.

I am not saying it's as easy as telling yourself "there is nothing to worry about" because that would be too easy and in your current situation probably not very helpful because you first should realize that your beliefs and concerns might be questionable. If you can get to that point, perhaps you can get to the second one in time: identify your system of beliefs.
You already have so much insight - you know where your beliefs and feelings stem from, you have identified the source of your jealousy feelings, your anxiety etc.. You are very smart as I have realized in many posts I read from you.
But I also think that sometimes you might create more suffering for you subconsciously because you have your mind already made up how you will feel and what you will be like in certain situations.
What if you turned it around?
What if you rewrote your post for yourself and turn the fears into possibilities? What if the new mentor really likes you?
There is a baby, you already know that. And you also know that a baby needs much more care than an adolescent or adult. It's nothing unusual, it's good, it's healthy and it's something you KNOW. "Competing" with a baby will almost always make you lose. If competing however transforms into getting a new little person in your life to love, to hold, to play with - it can become a gain, even a healing experience.
Perhaps try to make yourself more open to letting a part inside you become the carer of other people, like the baby. To make a choice to step back just a little and instead of fearing to not be loved enough, make an effort to love back more. I know how empowering, transforming and healing that can become.

Give the situation a chance, but perhaps before you enter it, try to change the beliefs about it a bit a little. I have learned the hard way that the more someone actively craves attention and love, the more other people withdraw or get uncomfortable and we might end up feeling lonely, isolated and rejected. But the more you truly love back without expectations, the more others will pick up on it and find it easier to give you what you need.

Well, just my opinion..

Lots of love and good luck!