another picture.

It's hard to tell what is wrong. Too much sun, too much fertilizer, not enough fertilizer, too little water. My first thought is it looks dry. What kind of potting mix?. Some raspberries don't do well in heavy heat, decrease sun exposure, add compost, then mulch to the top. I suspect the soil is too hot. Shade it with mulch, The pot is light colored that is good. A shade cloth would be excellent. So the sun is not as intense. Compost will keep the soil moist longer.

It is confusing as conditions are not severe, it should be doing better.

Thanks for your response, Drew51. It's confusing to me too.

Out of desperation, I gently dug it up today and noticed that the roots haven't developed AT ALL since I planted it 6 weeks ago--even though the leaves grew (and you will notice in the photos that it flowered). So it does look dry and I think maybe partly because the roots haven't developed. (Though, maybe 6 weeks is not enough time to expect roots to develop?--- I know nothing about this kind of plant.)

I will try to get it more shade--it can be moved to another part of the balcony--and I will mulch the soil.

The potting mix is a standard Miracle Gro mix -- I don't have the label anymore unfortunately. I have not added fertilizer to it but that stuff is pretty full of fertilizer when you buy it, so I didn't think it was necessary. It may be too much, but I didn't notice any visible damage to the roots. Just that they haven't developed.

Could this just be a dud plant? I hate that possibility but I was very surprised to see that the roots hadn't grown at all.

The roots should have grown. It could have a virus. But it is impossible to tell. Their is a product called soil moist, you put it is near the roots. It holds water and it pretty cool stuff.
Mulching will help. it's hard to mulch a pot, plus hard to tell when it needs water. I myself use pine straw. You may have a pine somewhere near you with ton's of needles underneath that you can harvest. Some are hard and spikey, others are soft. The soft are a lot easier to work with. These plants grow like crazy and that pot is not too big, that plant will fill it easy with new canes.
I grow lot's of raspberries but not in pots.
Here are my beds, notice the pine straw. The long section on the left side is raspberries
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Here is the same bed 2 months later
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I thought these things should grow better based on what I had read. Your photos confirm my suspicion.

I am wondering if the soil is getting too hot as you mentioned earlier and that's what's kept the roots from growing--would not be a problem in your garden because your plants are in the ground. The temps here are pretty moderate because of the ocean but the sun is still pretty intense. So I think the idea to mulch might be my best bet, to keep the soil from getting too hot.

I was wondering if it was a virus but I still have a feeling that is the less likely scenario.

Thank you a ton for your input.

Be patient, don't give up, and keep us updated. These are resilient plants if conditions become more favorable the plant should respond. You're learning a lot too!
Then one day you get to harvest! Yeah!
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You water every 1-2 days and the soil top and plant leaves look dry, as well as you have confirmed that there is not much root growth. But compared to saying "hardly any roots growth, but there were some" or "no roots yet" from 6 weeks ago, that will be some difference also.

You also commented on the "leaves on a stick" part. It seems like it is a cutting that could still be needing to create its roots. In that case, I may suggest to treat it like a cutting.

To do that, put it in a smaller pot so you can control water coverage better (for example, compared to saying the top part of soil is dry but the inside of pot is still moist/wet)

Give it some humidity by covering it with some clear plastic, propped up by sticks if you need to. Fasten that plastic to your container by tape or some other material.

You can achieve the same if your new container can it inside a ziploc bag that you would control humidity by opening/closing the bag.

Keep the plant in some light shade for a few weeks until it establishes a better root system.

Search the web for some term like "how to grow cuttings" if you want more detailed information or better steps than I have summarized here.

Thanks for your message, gardenper. The soil does look dry in that photo, because I took the photo before watering. Usually, I wait for the soil to become about that dry before I water; it is still somewhat moist underneath.

When I put the plant in the pot, it had a small root system. I do not know how to describe it, but the roots were an average of maybe 1 or 1.5 inches, with few of them longer than 2 or 2.5. So, it had been rooted prior to my purchasing it. I think the idea was for that root system to continue to develop in the soil.

When I dug it up yesterday, the roots did not seem like they had grown substantially. I cannot say if maybe they grew a little bit because I don't have a photo of what the root system looked like when I planted.

Attached is a photo of the directions that came with the plant for potting it. I followed all of them, except for the instruction about watering once a week, mostly because I did not think that would work for a potted plant.

Do you still think I should treat it like a cutting?

I would not treat it like a cutting myself. it has roots. I would move it to a shady location and slowly expose it to more sun once it starts growing some. Otherwise leave it in a shady location. Let's assume it needs to be hardened off, grown in a green house. This quick exposure to full sun might be the problem. Although I have never had that problem with raspberies.
You can do things to make the roots grow, use soil moist, add some rooting hormone, or add mycorrhizal fungi.
Don't fertilize till it starts growing on it's own. Oh i see the package says that, good advice!