If the problem is truely linear, it should converge in 1 iteration (one eval + one gradient correction).
I guess with the incremental Newton solver it might take 2 iterations, as it has to build the residual.
If you chance the convergence criterion to residual, and use direct solvers for the linearized problem, it should converge in a single iteration.
If you find this confusing, I would read: Custom Newton solvers — FEniCSx tutorial
and think about what this means for a single variable problem:
Content - Newton's method.