In the project samples, what is the rationale behind dividing the force by 1e4 in the EQ0Constraint in the Optimisation.bic files? Does this division aim to scale down the force, thereby artificially reducing the error and allowing for a broader range of acceptable solutions?

This is correct, but there is one other reason for that division. The optimisation algorithms do not work very well if the order of magnitude between the constraints and the cost functions are too different. Also, the termination criteria are relatively arbitrary, and it can be difficult to know if gains are due to model noise or if there are actually more gains to be made.

For this reason, it is good practice to normalize the optimization algorithms entries.

Note that with the NLOpt solver, equality constraint tolerances could be adjusted but it is preferred to divide constraint equality to obtain the same order of magnitude between parameters, cost, and constraints.