Hi,

first of all, can you please post code that one can directly copy into a notebook to reproduce the calculation. Screenshots are not good for that and no one really has time to retype everything by hand.

PaXEvaluate uses Package-X which is not being developed/supported since several years. And it never was open-source. So one should always expect issues popping up unexpectedly. But to say something definite I need to reproduce the error fist. Vanishing Gram determinants shouldn't be an issue, though. Direct evaluation of the scalar functions usually works without problems.

Should I enforce additional assumptions (e.g., on-shell conditions, dimensional regularization) before evaluation?

Ideally, you should enforce all kinematic constraints before the evaluation. It helps to simplify the calculation and make the output more manageable.

If I aim to extract the ​​Wilson coefficients​​ from this Lagrangian, what would be the recommended workflow? For instance, is there a built-in FeynCalc utility to match the amplitude to an effective operator basis, or should I proceed manually by comparing tensor structures?
Diagram

There's nothing really built-in for that, I think that everyone just writes they own custom code using the existing functions which does the job.

There are a lot of packages that specialize on calculating Wilson coefficients from the matching and offer all kinds of automation, so I'd look into that direction if you need to do the matching for multiple models.

Cheers,
Vlad