Best way of going from Frankfurt to Zurich in the first days of June 2020? (COVID-19)

In April, local and domestic train traffic was very strongly reduced, long-distance international bus traffic almost completely stopped but both are slowly resuming operations. Time and capacity are still restricted.

Specifically, for your route:

• Train traffic is more-or-less back to normal
• I couldn't find any bus, I tried well-known local operators like FlixBus and the search engine busbud.
• There are flights to Zürich.

Wearing a mask is mandatory in trains in Germany, strongly recommended but not mandatory in Switzerland.

PS: I am strictly limiting myself to the question you are asking. Since you were in touch with the relevant embassy, I assume you know there are still restrictions on entering the Schengen area from outside Europe and entering individual countries (especially Germany) but you are satisfied that you qualify for an exemption.

Train travel in Europe is fast and comfortable, and trains run extremely frequently, even in this exceedingly odd Coronavirus period of time. Except between roughly midnight and 6am, you'll probably be able to find at least one trip per hour between Frankfurt and Zurich.

Here's a list of trains on 3 June (starting from 8 am) from the Frankfurt Airport train station to the Zurich main station:

https://reiseauskunft.bahn.de/bin/query.exe/dn?ld=40143&protocol=https:&seqnr=4&ident=ln.024926143.1590677516&rt=1&rememberSortType=minDeparture&REQ0HafasScrollDir=1

While there don't seem to be any direct trains, there are several options that only require a single train change in Mannheim or in Basel Badischer Bahnhof, a German train station in Basel, Switzerland.

The "forecast" for all of these trains on the Deutsche Bahn web site shows very light traveler density, so you probably don't need to bother reserving seats; you can just sit where you find a place.

The trip takes about 4 hours and will cost just over €100 unless you're eligible for some sort of discount.

You should check before you go to make sure you can actually fly to Frankfurt, and to make sure you'll be able to enter Switzerland. Have a look at the What exceptions apply to this border closure? on this linked page to make sure you meet the requirements for entering Switzerland.

It's possible you won't encounter any border control between Germany and Switzerland; the trains don't actually stop at the border, but at train stations before and after it. But there could be border guards on the train between Basel Badischer Bahnhof (German train station in Basel, Switzerland) and Basel SBB (Swiss and French train station in Basel), so be prepared to justify your entry into Switzerland to them if you need to. (It's likely you'll be able to find one who speaks English.)