How many days in Trier

I suspect you are referring to Föhren (Foehren is the alternative spelling) and Naurath.

Not sure what you want to see/do exactly - and that of course will determine the length of your stay.

The Mosel River between Bernkastel and Cochem is pretty spectacular... old world villages, wineries, river cruises. It can be a nice place for biking if that's how you hope to see the countryside. Saarburg is quite nice... The Völklinger Iron Works, like parts of Trier, is a UNESCO World Heritage site. There is a German WW II Bunker in Irrel and another in Besseringen. Luxembourg - the city and the country - might interest you - and George Patton, along with many other Americans, lies in the American Cemetery just outside Luxembourg. So this could be stay of a couple days or a couple weeks.

Russ had a great response.
I suggest about 4 days to include Trier, Luxembourg city and Vianden as well as you family connection places.

to see everything and take in the countryside?

What is everything? Which countryside?

The one city and two towns? The Mosel valley? Wineries? The entire Rhineland, which would include the classic Rhine River Valley between Mainz and Koblenz? Festivals? Castles? History? WWII, Roman or something in between … like the Holy Roman Empire…which might take you elsewhere.

We spent a week from Trier to Koblenz and Boppard on the Rhine. Didn’t see everything.

Do you still have family in the area?

I should give you a more considered and considerate reply. My earlier reply was meant to suggest that you consider what there is to see. But it was less than helpful.

Only been to the area once, this past September, so I am no expert. But I can say that Trier has a great museum that includes a lot of the history of Rome in this area, close to 2000 years ago, as well as some Roman ruins. Definitely worth spending some time, there, particularly the museum. Also there is the church that Emperor Constantine established in Trier in the 4th C., as well as a Gothic Cathedral and a market square.

We cycled the Mosel Valley and there are many nice towns, vineyards, lovely countryside, and castles at Cochem and Burg Eltz, a relatively short bus ride from the river.

We did not spend enough time in Koblenz to see its museums or cathedral. But it has a lovely medieval city core that was far more intact than I expected after WWII.

See Rick Steve’s stuff on the Mosel River at https://www.ricksteves.com/europe/germany/mosel-valley

Thanks for your suggestions, everyone. When I said "everything" I meant the old historical things - I also need to find the church where my relatives are buried. But mostly the historical parts of Trier. We had contact with one of my grandfather's cousins, back in the 80s, but when my brothers met their children ( so about our age), they had less than zero interest in engaging with them, so no contact with relatives.

All the "old historical things" in Trier are here:

https://www.trier-info.de/en/places-of-interest

We spent 3 days in Trier, which included going on a walking tour from the Tourist Info. Seems like we saw all of the important landmarks there, and the churches and museums.
Enjoyable, fascinating town.

I can't comment on the countryside outside of Trier, but I was just in Trier itself, and one full day was enough for me. Maybe give yourself two if you really want to see everything and feel like one day isn't enough. Keep in mind that the Basilika is basically an empty shell and doesn't take long. I was in and out in 15 minutes. The Porta Nigra, kind of the same, unless you pay to go walk around inside and even that won't take long. Note that the Porta Nigra is currently having work done and much of it may be behind scaffolding when you're there if you are going soon. By far, the most time for me was spent at the archaeological museum. I was there for maybe an hour and a half, but you could conceivably spend much longer there if you really want to take in every little thing.