I did go to Germany to be re-united, but it was in the fall, before the mutations broke out. Still, what I learned may help (it went great by the way), as Covid was raging here if not so badly there.
1) Bring printouts of your form & invitation, and a few photos of you together. It helped not having photos only on my ipad/iphone.
2) You‘ll need them at hand at the USA airport flying out. I flew out of Seattle (to Frankfurt). Lufthansa‘s ticketing stateside went through them to permit me to board, so keep them near your passport. They will tell you if anything is changing day-to-day. If anything is funky, you‘ll know before you board.
3) German customs was great. I was glad I had printouts, they just took a couple minutes to check them & check you out.
4) You will take a test at the airport. By this I mean the last airport ( I went through customs in Frankfurt, but flew to Hamburg and got my test there). This took 2-hours! Long line that day, but it can be short too. So grab food or coffee between customs and the test just in case.
5) My destination, I immediately called the local health office. I think that gives you points because they were extra kind and knocked a day off my (in Sleswig Holstein, each state will have a different rule) 2nd test on my fifth day, which got me out of quarantine. Which was with my girlfriend, but I didn‘t leave her home.
6) I followed quarantine rules. Glad I did, they paid me a random visit. So follow whatever rules your destination requires. Also, I called them once a day during the 5 day quarantine to check in, let them know I had no symptoms, and pass them my last test result when it came & confirm I was freed from quarantine.
The German authorities - both customs & the health department - were terrific & knew about the reunion laws and helped all the way. All tests, even at my destination (Kiel), were free and well organized. Be kind and patient & they‘ll help you on your way. Everyone is happy to be part of your love story, so include them in your joy and expect good things!
My hardest moment was checking into a hotel in Hamburg, near the airport, on my return flight. They wanted copies of all my tests ( I had accumulated 3). I had gotten used to being free to wander without such things and had to scramble to find all three and email them to the hotel registrar standing in front of me before they let me take my room. So, wierdly, this particular airport hotel took longer than customs or health officials! So keep your test results handy as you travel! I didn‘t have access to a printer, but if your friend has one, print all your tests and keep them with your passport too. Just in case...
Also, I took a test before I boarded here on my way over...It wasn‘t required when I flew (maybe it is now?)... I‘m glad I did, as it helped when I got to Kiel. The local health people included that test in their calculation for quarantine release, which also saved me time. So get one just before you fly if you can. I called my health provider 2-weeks beforehand and, to my surprise, they made an appointment to get a 24-hour test set up before I flew. I had no idea! So call and set that up now if you can.
At the time, I was free to travel Europe and went to Denmark & back. That part was changing even as I left, so you may not be able to cross Euro borders, depending on the day-to-day.
So go! Don‘t worry, and look forward to your reunion! June‘s a ways ahead... things may be lightening up by then too... congrats on your reunion plans.