I suggested the Pi or Arduino since they are low cost and have a lot of available interface boards of various types available.
Either should be more than capable, which one probably comes down to what is in use at your place.
Although possible to electronically link two controls using old school analog technology using a computer for the logic greatly simplifies thing, especially when adding features and dealing with unforeseen issues.
1: Thought experiment: Left side stick moves, your system moves the right side stick, how does the system know who moved it and whether to in turn move the left one. If not properly tuned and designed very easy to get positive feedback, aka an unwanted oscillator.
2: From my limited knowledge at least some linked yokes are designed with a break away feature to handle potential jams. What is the equivalent in your system?
A lot easier to implement in software than pure HW.
Final question: Is the class goal primarily to demonstrate adding a feature to an existing system or is it to improve safety, either one is totally valid but the approach is different for each.
Improving safety will require finding an optimal solution, not just replicating an existing system.
This will require understanding the reasons side sticks were introduced and how best to improve situational awareness in that context.