Upvote:2
Three issues to consider:
The right to travel inside the Schengen area for short stays. If you have a long-term visa or residence permit from a Schengen country (that would be the case of your student visa while it was still valid or of your future residence permit), you are allowed to travel to Germany, for any purpose, for up to 90 days.
Unfortunately, temporary documents issued upon application to bridge the time before it is processed are often excluded from these rules (sometimes there is a distinction between a first application and a renewal in that respect). You did not specify which document if any you currently hold and I could not find anything relevant in PRADO but without a proper visa or residence permit, going to Germany (for any reason and any duration) seems risky.
The right to work while in Germany. Going to Germany for professional reasons is perfectly fine but they must fall under what's typically called “business” travel, which is not quite the same as “work”. This would typically cover things like meetings, trainings, negotiations, attending company events, trade fairs or conferences but not doing your usual work or replacing a German-based employee of your company. The fact you are going for a few days suggests you might be OK but you have to make your own determination and be careful with the way you are representing it.
On the other hand, if you actually have to work in Germany for less than 90 days, say complete some month-long mission for a client there, you can still do it on a regular Swedish residence permit or long-stay visa but you might need a separate work authorization from the German authorities and possibly additional documentation related to your employment and insurance situation in Sweden.
The COVID-19 situation. There are stringent restrictions on travel within and between countries in many places in Europe, although Germany and Sweden are among the least restrictive in that respect. But the German rules seem quite complicated. There are official restrictions on travel from outside the EU and additional checks on some land borders, but not all, which suggests there are no blanket restrictions on travel from the EU to Germany.
Where the checks and limitations do apply, there are exceptions for work-related travel but it's not completely clear how extensive they are. Some webpages suggest they are mainly intended to cover cross-border workers in essential sectors, others are more inclusive. Healthcare and transportation are included everywhere, the website of the Bundespolizei also mentions the food industry and “specialized contract workers” (mostly in the construction industry). At the federal level, business travelers (“Geschäftsreisende”, without additional qualification) are exempt from quarantine requirements and many seasonal workers have been flown in from Romania to work in agriculture.
In practice, the decision is in the hands of the police and they have quite a bit of leeway in deciding whether travel is justified or not. You need to take any relevant documentation with you (work contract, etc.) to support any claim you might want to make. All this also means that checks are likely to be more thorough so you might be asked to justify things that would otherwise just fly under the radar (like your exact status in Sweden and the nature of the activities you are contemplating in Germany).
You also have to consider a potential quarantine when returning to Sweden and the possibility that the situation could change while you are outside of the country, which could put you a in a very precarious situation (worse case scenario is being stuck in Germany in an expensive hotel with the clock on your status ticking or no way to complete formalities required to secure your residence permit).
None of this means it's a good idea to travel, obviously. The first thing would be to check with your employer how urgent or necessary this trip really is and if alternative solutions (like videoconferencing or postponing the trip by a few weeks) could be considered.