AW33 congrats on med school, well done! Smart move planning a trip before you are buried in hard work for the next 8 years or so. And then family maybe, big purchases, could be a minute before you can get back to Europe. As such it's good you are looking for advice; many solid suggestions so far.
I'm a 54 year old professor at an R1 university who's planning a 14th summer trip to Europe this coming summer. First trip when I was 20 years old college drop out. I've also travelled extensively and led a number of study abroad programs in South America. I have a pretty good idea what makes for enjoyable travel for young people.
First: solo or with a group? If so how many? The answers to these questions make a difference.
You don't rest away jetlag. You active away jet lag. People debate whether a nap that first day is a good or bad idea (I'm agnostic - solid result both ways for me), but being outside moving around in the daylight gets you over jetlag and resets your bio clock faster than anything else. Tire your body out moving around on day one, sleep better night one, get on local time quicker. Get to somewhere you want to explore and get out there. Walk up to some castles maybe.
Plan a touring trip like the one you're planning with a "go deep/short blitz" strategy. Do three nights in a couple/few places you want to explore extensively; roll through other places with a quick look around. Don't feel like you need to cut out a full day for any given place if you wonder how to fill it, or if you are taking away from being able to spend more time somewhere you want to go deeper.
Hallstatt is a dead end that will take quite a bit of time relative to the couple postcard quality views you'll get and the throngs of tourists you'll battle. Save it. If I was going to stop at one place between Salzburg and Vienna it would be the superlative Melk Abbey, which could be argued the greatest high Baroque site on the planet. Gold leaf and marble absolute madness, very beautiful and interesting.
Hallstatt is in the foothills, and the Dachstein is a big beautiful peak, but it's behind big foothill ridge from Hallstatt. You can't really see it. You could see it from Gosausee, but that's an even more inconvenient dead end than Hallstatt. If you want an alpine experience that's close to your current itinerary think about Berchtesgaden. Close to Salzburg, Berchtesgaden has views of (and access to) high mountains, a crazy beautiful ultra-clean lake, and lots of 20th century history (it was Hitler's mountain headquarters, chosen because the raw alpine beauty and traditional culture fit his idealized notion of what being German was. Nonsense of course, but he did pick a gorgeous spot). If you'd like ride a gondola to hike among the edelweiss, I'd find two night to go there. Many other alpine spots are good too, and not so far from Munich.
Figure out if you want to meet fellow travelers or not. If so, plan your trip around the more social youth hostels/spots, particularly in the "go deep" places. Much easier to meet people if you'll be around for a couple of days. I met dozens of great people and had dozens of crazy, fun experiences of all sorts when I was single and on the close to the ground backpacker circuit. If you'd rather keep more to yourself that's fine too, but know that you'll have far more options to hang with people if you aren't always on the move and staying in hotels alone.
Traveling from place to place doesn't connect points in the trip. It's all the trip. You likely won't do this, but if I were you I'd skip Salzburg, head to Passau instead (cool Baroque city in its own right) rent a bike and ride the Danube to Vienna, or at least to Krems and then train to Vienna). The ride is chock full of worthy cities and towns along the way, and you see country life too. By the time you arrive down river in Vienna you understand Austria. 4 nights, worth it, won't be a blur in memory.