2-week train itinerary from Istanbul to Berne in April

Unfortunately, there's not much train service in a lot of the area you want to cross (the Balkans), and in many cases what there is, is slow. Honestly, I suspect you'd do much, much better to get a refund on the Eurail pass--even if you only recover part of the cost. Then you could spend your money on buses and flights as necessary to supplement the sketchy rail service. Until you get into Austria/Germany and especially Switzerland, the trains are as cheap as they are slow, so the rail pass is not remotely a money saver along this route.

There are tons of interesting places along the way between Istanbul and Bern if you look at a map, but they are not necessarily well-connected by train, or connected by train at all. Two weeks would be enough time to see only a very few of them, anyway, even if you could hop around by train at will.

You can get at least a vague idea of the rail routing you'd need to use, especially the gnarly section through the Balkans, by looking on the Deutsche Bahn (German rail) website. They don't sell tickets for most of that territory, but they attempt to show the schedule options. https://int.bahn.de/en. Use your logical starting date in April (try to be correct as to whether it's a weekday, Saturday or Sunday) and you'll see one recommended departure time per day, at 8 PM. The entire itinerary would take 50 hours, an average of over 3-1/2 hours per day for your two-week trip. Click on "Detail" to see the basic routing, showing where you'd be changing trains (starting with a 4:43 AM transfer in Dimitrovgrad, Bulgaria, where'd you'd be waiting around for over an hour). Then click on "X stops" for each segment of the trip, "X" being a number, to see a list of all the towns where the train will stop.

Night trains are not a favorite of mine at all. They may be decent on some routes; on others, there can be many stops during the night, each one accompanied by braking, station noise and acceleration. Not everyone can sleep through that, and if you do not, you may crash the next day and be off-cycle in a way that feels a lot like the miserable (to me) aftermath of an overnight flight from the US to Europe. I hate that, and I have no desire to go through it again in the middle of a trip. On this particular trip the first leg has 6 stops between midnight and the 4:43 AM transfer in Dimitrovgrad.

An additional issue with night trains is that sleeper berths (and occasionally even couchettes) can sell out well in advance.

I can only hope the rail service is better in Bulgaria and Romania than it was for me in 2015, at which point some trains that were supposed to be running were not. I met a tour group from Canada on a supposed train itinerary who were suffering through either 2 or 3 overnight bus rides because their overnight trains weren't running. The trains I took averaged about 30 mph, and I didn't have to deal with linking Turkey and Bulgaria.

At a more basic level, there is little rail service across borders in the Balkans, so it's not at all like traveling in the countries to the north and west, where you have lots of options each day.

I urge you to rethink the whole concept of this trip. There's not a good match-up here between the area to be covered, the time available and the plan to use only one mode of transportation.

I've never done it, but a few people on the forum have used private drivers in some of the tough-to-traverse parts of the Balkans. That would be a lot more comfortable, I suspect, than what you're contemplating, and possibly not as expensive as two rail passes if used judiciously.

I had a nice time using mostly public transportation in Romania and Bulgaria in 2015, but I spent 4 weeks doing it, and I used a lot more buses than trains because they were more efficient (in some cases, because they simply existed when trains did not).

It is to be assumed that if you are thinking of such an itinerary you, like me, are perfectly able to sleep and sleep well on overnight trains.

Very many people do, and some people don't.

This is a journey I have long been trying to do- as part of an even longer trip by train to Syria or Iran (both currently not possible). Really the time has come now to admit that Turkey is as far as I can get for the foreseeable future.

Look at Man in Seat 61 for how to do this, and also how to book the train which uses very modern TCCD (Turkish Railways) sleeper cars and couchette cars- https://www.seat61.com/trains-and-routes/bucharest-and-sofia-to-istanbul-by-train.htm

Firstly the pretext of changing trains at 5am is NOT correct. That train extends to Sofia after a 2 hour 18 minute wait at Dimitrovgrad and arrives at Sofia at 1047. From, June to October through cars also go to Bucharest, arriving at about 1700.-

You do have to go through Turkish border exit controls at Kapikule at 0105 to 0220 where you get off the train with your luggage and go through the passport physically in the old fashioned way. By all accounts this is an efficient process, but the train can be held if there are illegals trying to make the journey.

From Sofia you take a day train at 0700 to Ruse- arrive at 1331. You can break your journey here overnight or switch trains departing at 1415 and arriving at Bucharest at 1717. In summer this is a through train. I would suspect there may be earlier Ruse to Bucharest trains.
Sofia to Ruse is by an elderly loco hauled train with corridor style compartments (yippee- some people decry these, but even the brand new OBB Railjet Mk2 has some compartments, by popular demand). From Ruse it is a modern DMU.

https://www.seat61.com/international-trains/trains-from-Sofia.htm#Sofia_to_Bucharest

From Bucharest onwards all journeys can be booked on the web. There are a couple of overnight trains a day to Budapest- the modern and by all accounts very nice Ister (with restaurant car) or the Muntenia (with older cars, and no catering)- I sure know which I would prefer (the Muntenia). Now Man in Seat 61 concentrates on trying to do this as a through journey.
But it is entirely possible to stitch that leg together using day trains, and an overnight stop or two.

Once you get to Budapest the world is your Oyster in terms of train routes and types of train.

If you have never taken an overnight train, and depending where you live in the US, try an Amtrak one night overnight service as a weekend away or a short vacation.

In the North East the restored DC to Boston route is one possibility, or one of several DC/NY or Boston to Chicago routes. Then fly home from Chicago.

On the West Coast part or all of the Coast Starlight LAX to Portland (OR) and Seattle via 'Frisco.

Or an overnight segment of one of the Cross Country routes- fly into City A, overnight train to City B, fly home from City B after a night or two there.

Or try the auto train from Sanford to Florida- where you take your car with you to Florida on the train. You could do that one way then make a road trip out of the other direction.

This feels like phd travel with a HS diploma. The Man in Seat 61 is your best resource.

You've said you want brief city stays, so try (as an example)-
Day 1 depart Istanbul
Day 2 arrive Sofia
Day 3 Sofia to Bucharest by day train
Day 5 Bucharest to Budapest overnight
Day 8 Budapest to Vienna on one of many trains (all trains beyond Budapest are high quality day trains)- you could even route through Bratislava for a one day visit.
Day 10 Vienna to Salzburg or Innsbruck
Day 12 Salzburg/Innsbruck to Munich
Day 14 Munich to Bern via Zurich

From Budapest you could instead route through Prague.

Or maybe Day 8 Budapest to Zagreb
Day 10 Zagreb to Salzburg (even add in a stop at Ljubljana)- both these days are on Euro City trains
Day 12 as above