Magic Jar required a component to hold your soul as part of the spell. However, Wish allows you to forgo a spell's components when duplicating them. How can one possibly cast Magic Jar using Wish?
It's just a contradiction, requiring the DM to make a ruling.
There is no explaining this one away. Wish ignores the material component of magic jar, and the spell description of magic jar utilizes that material component as part of the effect of magic jar. It's just a contradiction. The DM will have to make ruling. As it says in the introduction to Xanathar's Guide to Everything:
One rule overrides all others: the DM is the final authority on how the rules work in play.
The DM is key. Many unexpected events can occur in a D&D campaign, and no set of rules could reasonably account for every contingency. If the rules tried to do so, the game would become a slog.
Sometimes the rules don't make sense, but the rules have given the DM the power to make sense of them for us. As I explained in my answer here, wish should trigger some conversations between the player and the DM about its use. If you plan to try to use wish to cast magic jar, talk to your DM first, so that they have time to think about the decision rather than ruling on the fly in play with a ruling the table may regret later.
You will run into a similar contradiction with any spell whose description explicitly uses the material component such as:
- booming blade
- green-flame blade
- instant summons
- plane shift
- conjure barrage
- conjure volley
- cordon of arrow
- create magen
- dream of the blue veil
- Jim’s glowing coin
- Leomund’s secret chest