What is needed to compute the ionization energy of hydrogen from the full Standard Model? [closed]

Many quantities computed from the Standard Model agree with measurements to amazing precision. For example, the electron magnetic moment, as well as the ionization energy of hydrogen. Focusing on the latter, the computation from the Standard Model (and even just from QED) is very complicated. As far as I know, there aren't even self-contained and complete presentations of these calculations.

What would it take to state this computation as an algorithm?

In particular, what must be supplied to the algorithm as inputs, and what can be asked of the result? I assume it needs only the Standard Model parameters as inputs. Things like the proton mass should be a QCD prediction. Ideally, the computation should be phrased such that all inputs, as well as the output are dimensionless.

I also assume one could ask for a desired relative precision with some limitations. First, the perturbative expansion is asymptotic, which should imply a limit on achievable precision no matter how much computation is permitted. Second, since this is a bound state problem, I think the result isn't a power series in $\alpha$, which seems to complicate the question what "order", and hence "precision", would even mean here. I would like an answer that addresses this.

I'm not concerned by the algorithm being practically executable. Rather, I want to know what it would look like to unambiguously state the computation. Computing clearly well-defined mathematical problems, such as convergent integrals or series, is assumed to be free.

I'm also not concerned with the precision to which the inputs (Standard Model parameters) are known experimentally, only with the computation itself.

I'm also not concerned by the fact that the Standard Model is not a theory of everything. I want to fix the meaning of "Standard Model" as much as possible beforehand and not worry whether the maximally precise prediction of the model can be expected to match ever more precise measurements.