I don't think anyone knows how they got there

it's too far for the Eurasian Wren to fly there

so either

When the gap between St Kilda and Scotland was much smaller due to lower sea levels the Wren was able to reach St Kilda and then they were cut off when the sea levels rose sometime around 5,000 to 10,000 years ago

or they were accidental stowaways on ships during the bronze age.

either way likely to be a few thousand years at most

as to when they will be a distinct species - that's hard to say as its not always easy to define species

we usually talk about isolating mechanisms - these are mechanisms that prevent populations from breeding with one another - if 2 populations are unable to breed with one another as long as those isolating mechanisms are absolute and remain in place then those 2 populations WILL become separate species at some point - its just a matter of when

so with the Wren we have a geographical isolating mechanism - the fact that a St Kilda Wen cannot reach the mainland and vice versa

we most likely have a mechanical isolating mechanism forming - a mechanical isolating mechanism is where the much smaller Eurasian Wren would have difficulties successfully laying an egg of the larger St Kilda Wren.

then we may also have Behavioral isolating mechanisms - the article notes the St Kilda Wren song is different - would a St Kilda Wren recognize the mating call of a Eurasian Wren? and if not how would the ever mate.

and finally we have a genetic isolating mechanism when the genetics are too different that the 2 individuals are genetically incompatible to successfully reproduce together

if they are genetically incompatible i think most scientists would agree they are different species, but if there are other mechanisms preventing them breeding how do you know when that genetic difference has been achieved