As of today, 24 March, Austria is opening another crossing on the border with Slovakia. The news concerns the crossing Angern – Zagorska Ves (north of Bratislava) 
As a reminder, most of the crossings were previously closed due to Covid-19 and lockdown.
For now, all restrictions related to border crossings during the pandemic remain in place in Slovakia.
At the moment, entry into the country is permitted if
Вы оформили через посольство Словацкой Республики национальную визу. Национальная виза выдаётся, если у вас есть конкретная цель поездки, которую вы подтверждаете документально. Это может быть: воссоединение с семьёй, учёба, работа, бизнес.
You have a residence permit or a residence permit in Slovakia.
Вы являетесь близким для человека, имеющего гражданство или ВНЖ/ПМЖ в Словакии. Это актуально для родителей несовершеннолетнего ребёнка, супругов, несовершеннолетних детей.
You are a citizen of the EU.
You belong to a narrow category of citizens who are also allowed to cross the border. For example, you need to care for a relative in Slovakia.
How can one even apply under such circumstances if one does not yet have residence permit, residence permit or citizenship in Slovakia?
In this case the national visa is relevant. The grounds for obtaining a national visa are often the same as those for obtaining a residence permit. Therefore, it is usually not a problem if you have already planned to apply for a residence permit in the Slovak Republic.
There is also progress in the situation with the pandemic. Now every tenth person in the country has been vaccinated. The number of people hospitalised with Covid-19 is gradually decreasing. I do not want to comment on these facts and give forecasts. But such news regarding the culprit of all restrictions is very happy 
