I looked at this earlier in the year (ended up taking TK via IST) but my understanding is that this Aktau stop has been forced on Air Astana because they can no longer overfly Russia and they don’t have planes capable of doing the longer routing - therefore Aktau is effectively a technical/ fuel stop. On that basis, and my understanding when I was maybe taking it, was that Air Astana were running it as an LHR-(Aktau)-ALA service, and therefore there was zero risk of not making the second flight.
tl;dr - OP, don’t worry 😉