I'll first describe how government formation works in Belgium and afterwards what is special about the current government.
The usual way of forming a government
As in many countries, it all starts with elections where the seats in parliament are distributed. Based on the seat distribution you try to create a majority. Important to know it that in Belgium the political landscape is very divided with many rather small political parties. Twelve political parties are represented of which the largest has only 25 out of 150 seats. A further restriction is that the number of Dutch speaking and the number of French speaking ministers must be equal. The fact that Flanders voted right and Wallonia voted left complicates things further.
After the elections the king gives a "formateur" the task of forming the government. This formateur presents his government, obtains the confidence of parliament and becomes PM. If it is not very clear who will become the next PM, the king can send out some other politician(s) who have the task to feel the temperature, find where there is room for compromise etc. Usually this are experienced politicians with lots of contacts accross the different parties. Style former senior ministers. Those guys often get very original titles like Royal Explainer, Royal Explorer, Deminer etc. Once it becomes clear what will be the next coalition, the king will name a formateur who can seal the deal and there is a new government. It kind of works, but takes an awful long time. A year without government is not that exceptional anymore.
Isn't it a problem that there is no government? Not really. The previous government just carries on as a care taker government, or a government in running business (NL: lopende zaken, FR: affaires courantes) as it is called in Belgium. That means that they can execute what was already decided, sign stuff that needs a signature, but not make real decisions. Also the budget becomes simply every month one 12th of the budget of the previous year.
What about Wilmès?
The last national elections were on 26 May 2019, together with the European elections. The outgoing PM was Charles Michel. Sophie Wilmès was the minister of budget. In December 2018 the biggest party in the coalition left the government. They tried to carry on as a minority government. That didn't really work and instead of trying to make a new government they became a care taker government because the elections were so close anyhow.
After the elections there were the usual attempts to find a compromise that would lead to a government. It was clear that it would take a while due to the big ideological differences between the parties that could mathematically form a majority. After the king had gone through two informateurs and two preformateurs, the PM Charles Michel got the chance to become President of the European Council and jumped to the opportunity.
Suddenly the care taker government needed a new PM. It didn't really mather who it would be as it was only until there would be a new government with full powers. All that mattered was that the new PM had to come from the same political party as Charles Michel. The honour went to Sophie Wilmès, with the bonus that she became the first female PM of Belgium.
Afterwards, the attempts to create a real government with full powers continued. It was not easy and the king named three more informateurs and then three Royal Assignment Holders. By that time it became clear that there was a thing named Covid approaching and that you would not be able to take the necessary measure with a care taker government. The pragmatic compromise was to keep the care taker government in place. This requires a vote of confidence in parliament, which would be supported by 10 of 12 political parties. The flip side of the agreement was that the government would, in concertation with all 10 parties, limit itself to tackling the covid crisis. On 14 March 2020 Belgium went into a light lockdown, on 16 March the king made Wilmès the formateur, on 17 March she won the confidence vote in parliament and became PM of a government with full powers, even received emergency powers, and on 18 March Belgium went into lockdown.
The covid crisis was an interruption, but the objective is still to have a government with real policies, taking real initiatives. Since May various presidents of political parties have been trying to forge a coalition. My impression is that things are not really progressing. But they keep trying.
For your questions: was it a default measure? Not really. It was more a pragmatic compromise. It turned out that any changes to the status quo provoked more discussion than there was time for.
Is she expected to resign? Yes. In fact she was not meant to be PM in the first place. When? As soon as there is an agreement for some coalition that has a majority in parliament. The expectation is that she goes to the king to throw the towel, the king accepts and names whoever is the PM in the compromise as formateur. And if she doesn't? Then she would lose a vote of non confidence in parliament and have to resign anyhow.
And what if no compromise is found? Then she will probably plod on. Or there might be new elections and she becomes a care taker government again. And what if she tries to set her own policy? She would lose a vote of no confidence, have to resign, become the PM in a care taker government and the king would name a Royal Something who has to prepare the terrain for a formateur. Practically speaking, all the different scenario's give the same result.