I think you will have to replace the dishwasher drain hose. The end is so scaled up and worn that I think it will be difficult to install it leak-free. But you may as well try. Replacing it will be a bigger job.
Here is what to try:
You say the end of the hose is metal. It SHOULD be rubber. Hopefully it's rubber, and it has hardened and just feels a bit like metal? The large end, iF it's rubber, should fit snugly over the disposal's unused port. If it really is metal, see if the smaller part of it (the other arrow in my pic) is rubber and fits? And the larger metal one is just slipped on? Then remove it. Either way, or by replacing the hose, you need to clean up the rubber end by scraping it and using a descaler or vinegar. Make it smooth and clean but without cutting slits or cracks into it. This has to make a seal over that port.
Your cleaned up (or brand new) rubber end needs to fit snugly over the small unused port on the disposal. You also need to install a hose clamp on it. Not a spring-clip hose clamp such as on the lower pipe, but a screw-down one, because it's under pressure from the dishwasher's drain pump.
Before you connect the hose to the disposal make sure the unused port was prepared by breaking open the seal. If you stick a pencil or screwdriver in the hole, it should go all the way in so you can see it through the bottom of the sink. The disposal is shipped with that hole sealed up, you have to unseal it by smashing off the plastic disk molded inside it. It's not always easy, and you might need to remove it from the sink and lay it sideways on the floor so you can hit the seal hard without the whole thing bouncing around or damaging your sink.
In the end it should look like this
Finally, read elsewhere about the "high loop" required for the drain hose. Basically, the hose needs to go up high above the disposal then back down to the disposal port. Read about it before doing the job.
If you end up having to replace the hose, look on youtube for tutorials on how to do it with your model of dishwasher. With different brands it can be very easy (a similar rubber socket on the back of the machine) or very hard (disassembling half the machine) or in between. If you're not comfortable with that kind of work get an appliance repair person to do it.