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You can, pretty much, plant anything else that isn't related to raspberries in that area. All rusts that affect raspberries and blackberries will be a permanent installment in the soil, and no treatment will kill it off.

Here is an article that will help:

https://www.gardeningknowhow.com/edible/fruits/raspberry/treating-rust-on-raspberries.htm

So sorry to hear about your snow disaster. If the canes are broken at the ground they absolutely need to be removed because they are vulnerable to all kinds of problems. You may have to start all over again with your raspberry crop. Here's an article that may be helpful:
https://www.gardeningknowhow.com/edible/fruits/raspberry/pruning-raspberry-bushes.htm

That's a ladybug pupa! Leave it there. They are very beneficial to your plants, and will eat pests that will cause harm to your garden.

Yes, I do see signs of overwatering.

Instead of watering on schedule, try watering when the container needs it. Once the soil dries down to about 3 or 4 inches, give it a nice deep watering. This take will vary depending on the climate conditions at the time, so measuring is important. Just stick your finger down to the depth of 3 or 4 inches and if there is any moisture at all... Hold back on watering. Alternatively, you can get a moisture meter to help.

Treat with a fungicide, then care for them as usual.

Here are some articles that will help:

https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

https://www.gardeningknowhow.com/edible/fruits/raspberry/raspberries-in-pots.htm

Unfortunately, raspberries are susceptible to many diseases that are not curable, and lifelong. This is probably the case here. You can choose to keep the plant around for an ornamental, but it is likely that you will have to find a more disease resistant cultivar, or plant blackberries instead.

Here is an article that will help:

https://www.gardeningknowhow.com/edible/fruits/raspberry/raspberry-canes-turning-brown.htm

You don't mention what the wrong spray was so I can't look it up. If you read the label, it should tell you how close to harvest you can use the spray and if it can be used on edibles at all. Some products, like Neem Oil can be used until the day of harvest.

If you don't find it on the packaging, call the company and ask, or call your local cooperative extension agent for advice.