Ideas for how to use sauerkraut?

I often chop and stir sauerkraut into potato salad instead of pickles; I make it like my mother used to make what she called "German" potato salad -- splashing the hot potatoes with brine instead of vinegar the minute they're drained. No mayo, just a touch of oil, after the potatoes have had a chance to soak up the brine. Add tiny dice of celery and fresh parsley -- and a small dollop of spicy brown mustard whisked into the oil, if the spirit moves you.
Non-vegetarians could (should!) add chopped bacon as well. ;o)

In a way this is a sad question to be answering because to me sauerkraut belongs alongside a piece of brisket or a sausage----like blood sausage. That said, I would go with something like poutine. Well made pomme frites make up for a lot of other sins. And you could make a "gravy" with a mushroom base.

I was thinking about Hungarian soup/goulash with sauerkraut (usually made with meat – could try subbing vegetable broth.)

Which reminded me of one of my favorite Korean dishes, kimchee/tofu stew - again leaving out the meat (pork) and replacing the kimchee with sauerkraut. Both are fermented cabbage and I’ve heard that sauerkraut came to Europe from China, thanks to Genghis Khan – so an Asian twist might be kind of interesting. (Even if that origin story were a myth!)

I do remember seeing a recipe year ago where sauerkraut was rinsed and drained, then toasted and used on the top and sides of a chocolate cake. I believe it was supposed to be kind of like toasted coconut.

I used to make sauerkraut sandwiches when I was in school - toast with sauerkraut, pickle relish, and mustard. I though it was ok and most importantly, it was cheap. If you aren't on an "end of semester" budget, I also like sauerkraut on eggs and over frittatas. Also, over stir fry. On pizza. Basically, if I feel a dish needs a little something, I reach for either sauerkraut or kimchi.

Make an Alsatian style pizza!

Make some Pierogi! Also you can certainly split in to portions and freeze it for later use..

If you want a project, you could make traditional Polish/Czech pierogi stuffed with potato, cheese and sauerkraut. Serve them with caramelized onions and a dollop of sour cream - heaven. (There must be recipes online.)

It's basically a pickle, so many things that call for pickles can often sub the sauerkraut nicely. It makes a great addition to sandwiches (think hamburger, hot dog, reuben and expand your worldview from there).

If you reflect on how other cultures eat pickled vegetables, you should be able to find additional opportunities.

That said, sauerkraut lasts a long time in the fridge, no reason to attempt to pound it down in a week.

Ditto on the tempeh reuben. I also like to saute it with apples and Field Roast Smoked Apple Sage (veggie) sausage.

Also in lentil soup . . . . . braise with white wine, bay leaves, juniper berries and onions . . . . . chop and mix into mustard (memorable when slathered on cheese sandwiches): https://food52.com/recipes/10853-opening-day-horseradish-and-sauerkraut-mustard
And as Emma noted below, put it in bread - rye bread loves sauerkraut: http://www.kingarthurflour.com/recipes/tender-sandwich-rye-bread-recipe ;o)

Soup: paprika-spiked broth, lots of mushrooms. Avocado toast: big sprinkle of toasted caraway seeds. Tempeh reuben: pumpernickel bread, all the Russian dressing. Salad dressing: blend with olive oil and fresh herbs (feel like dill would be pretty on-point here). Veggie "hot dogs" (esp a charred, whole-carrot one). Bread dough!