I’ve seen this mentioned before on LG, quite a few times and heard of people wanting to make their own ballast’s!
But this type of electrical engineering here seems to be steeped in secrecy and mystery! 🤔, people in Britain that can do it tend to not tell you much about it, i.e, the grade of wire, the wind numbers, the math that goes into it!
Imagine if you had the formula to hand to be able to make your own 200 watt SLI/H autoleak transformer, (something that is so rare in the UK, people have to use alternative gear)!
Maybe Roman (RRK) can shed some more light on this as he did above?😎
There is no secret or mystery in calculation of a transformer, including a leak transformer. All the math is already 150 years old

A tricky part may be there is no direct recipe to make a transformer or an inductor, you need get a balance of cost, weight, size and efficiency. All these parameters are mutually dependent! Add also a necessary 'fun' measure to a hobby project. Designing a balanced ballast may be an ok job professional, but too mundane to complete as a hobby.
First thing you have to respect in designing a magnetic part is saturation induction of a core, called Bmax. As Bmax defines a maximum of counter-EMF in a winding that works against an applied voltage, generally it will dictate a number of turns per volt for a given core cross section at a given line frequency. Okay. Next you have a turns ratio between primary and secondary approximately as a ratio of line voltage and OCV required. Note that in practical leak transformers secondary winding is usually fed from a tap of primary, so the ballast is in fact somewhat in between of a choke fed by an autotransformer and true leak transformer. Next you add a magnetic shunt. Calculating magnetic resistance is complex, one may even tune magnetic shunt gap experimentally.
And so on.
As for (re)making a SLI/H ballast. As usual, before you start to make anything, the first question to ask is 'why'. Depending on the answer you can go different ways. Let's say the answer is 'I just want to light up a rare lamp correctly'. Well then you have to remember that any leak transformer is electrically equivalent to a combo of an (auto)transformer and a choke. Making this is significantly easier than making a custom leak transformer. You can reuse some scrap transformer for an OCV required and then add a group of chokes calculated to proper impedance for prescribed lamp current.
Or the answer may be 'I want to have a historically correct replica of the ballast!" Okay then, the best you can do is to find a surviving original and take all the measurements. Turns can be measured non-destructively. Modern magnetic materials are likely slightly better than historical ones, so you may measure the core dimensions and re-create it with modern laminations.
Or you can answer 'I just want some fun)' Well that's legitimate for sure. Making a transformer/choke is relatively trivial. I did some at 50Hz and HF too. A winding machine is not complex and not very expensive, generally it is a bobbin holder with a counter and a hand or motor crank. Enamelled wire is easy to buy, even some modern varieties available, even off Aliexpress. You can cannibalize some scrap transformers for magnetic materials and coil formers.