Do you think her playing tennis with me would cure the control issues?
No. Why? Because she is with you and monitoring every move you make. If you even so much as smile and say hi to any woman, you will never hear the end of it. You need space
away from her, not doing even more things with her. And as you said, it spills into other areas so it's not about who you're playing tennis with. It's about her control. Play tennis with her, and you lose in her game of control. This is why boundaries are so necessary. Marriage is not about winning and losing a game of control. It's about partnership where you are together because you want to be together.
I agree with Hidden. By the sounds of things, you have been playing tennis a long time - long enough for her to know that there is no reason to be so distrusting. Might be an interesting conversation to have with her when she tries to control, is to ask "what are you so afraid of?" or "what's the worst that can happen?" If she says she is afraid you are going to be attracted to another woman, then you can say "is that really what you think of me? Do you really think I do not have the integrity to keep my vows?" If she has already formulated this kind of thinking, there will be little to nothing that you can do about it. You can't change her opinion of you, and if she is going to nurse her negative thinking and assumptions of you, then there is nothing left to the marriage. And there is the boundary - she can nurse her assumptions all she wants, but you can choose to not live with someone who does not believe in you (or whatever else you are going to do in order to cope with her negative thinking about you).
This is where a lot of abused people truly suffer - and you have already said you are losing your identity... you start losing your voice in the marriage. You start believing the abuser is right, and then eventually you lose yourself, you lose confidence, you lose your true purpose in life, you lose your own perceptions. You question everything you know to be true about you. Don't let this happen to you! It's so much easier to do in the early stages than if it's been going on for decades... please read the book Boundaries (or Boundaries in Marriage - either will do) by Cloud and Townsend. You are not responsible for her jealousy. You are not responsible for her control issues or for what caused them. You are responsible for you, and for how you respond to her attempts to control.
You are using phrases like "she is forbidding me to play..." and "she does not allow me to have friends..." I am assuming you are a grown man, so you do not need to ask permission. She is not your parent. It is a matter of courtesy if you simply tell her where you're going or what you're doing, but you do not need to ask permission. It should suffice to say "dear, I'm heading to the tennis court and will be home by (time)." That is how a mature person does marriage. And a mature spouse on the receiving end of that kind of comment is "thanks for letting me know. Have a good game!"
Ime, people like your wife, who frame everything you do with suspicion and negative assumptions, don't change unless they go for therapy, such as cognitive therapy, where she develops an awareness of her thinking and then use self-talk to combat the negative thoughts. And of course, people like this don't typically think they need therapy - usually these kinds of people blame everyone but themselves.
Praying for you.