You have already given him advice and guidance and you have communicated to him that his progress is behind expectations. He has also been given a warning at his first-year review. You cannot force the student to meet the required standard for the candidature --- your primary role as a supervisor is to give him a candid evaluation of his work and offer academic support and guidance where needed.
It is difficult to see if you have already done anything effective, because all you have told us is that you have given some (unspecified) guidance and that you have had multiple meetings to this effect. In any case, one thing that might be helpful here is to have the student create a scheduled plan for what he will achieve by the time of his next review, and meet with him regularly to get updates on progress. You should ask the student to set out his own plan and schedule to achieve relevant research outcomes and construct a Gantt chart setting out the schedule (you may need to give guidance on this). Be inquisitive about the student's own expectations and goals. How does he see his progress so far? What things would he like to achieve and by when? How will his plan and schedule manifest in successful completion of his PhD candidature? Is his plan realistic? Has he included sufficient time for each part of research? Will he be ready for the relevant milestones? What does he plan to achieve by the time of the next review milestone?
Another thing that is worth considering is whether you might want to involve another academic to review present advice/actions and give their own perspective. If you are giving the same guidance over and over and this is not being actioned then it is probably worth bringing in a "second opinion" from another academic. Either this other academic will regard your advice as accurate and will reiterate this to the student, or they might come up with some other ideas that could potentially help the progress of the student. Don't be afraid to lean on your colleagues when dealing with hard cases.
Furthermore, he is now going to take a five-week vacation and go back to his country, which is permitted according to our doctoral school rules. I know that this break will slow his overall progress even more and upon his return he will need additional time to catch up to his current status.
If the student is taking approved leave under the rules of the school then this should not be considered to "slow" his progress. Leave always necessitates a period of catching-up when one returns (e.g., actioning emails, etc.) and this is part of the normal activities that surround the taking of leave. The expected schedule for progress should take account of the fact that students will take approved leave and that this will necessitate certain catch-up activities on return. If this is not properly taken into account then it is a managerial failure, not a deficiency in the student.
I know that as a foreigner life might be difficult per se, so I do not want to stress him out by consistently pushing him to follow my guidance.
Declining to give the student candid feedback and proper expectations for progress will not reduce stress in the long-term --- it will just set the student up for failure later, which will induce stress at that time. It is generally a bad idea to try to calibrate your scholarly guidance to account for the presumed effects of some exogenous circumstance you don't understand well. Either your guidance is giving good advice or it is not. If it is good advice then it should be delivered irrespective of whether this student has a difficult life. If it is not good advice then it should be altered accordingly. As to "pushing him" to follow your guidance, this also overstates your role. PhD students are adults who are capable of considering what guidance to follow and what guidace to ignore. The student has been warned that he is behind expectations and he has been given guidance for what to do to catch up. That is a sufficient amount of information for the student to make an informed decision of how to proceed.