Alfalfa is especially good for adding nitrogen, but clover can do the same for a home garden.

You are correct on the number of years between plantings, but really only 2-3 years off are needed to clear the fungus. Alfalfa just lasts longer.

As another comment mentions, some other common crops have the same disease risk, so avoid potatoes and eggplants too many consecutive years.

Fallowing it an option, but a little nitrogen for a home garden shouldn’t be too prohibitive. When you have a lot of acres it can be a meaningful cost saving measure but it’s not huge.

I have this issue right now with my tomato plants. Am I right in my understanding that you don't necessarily need to crop rotate and just supplementing the soil with nitrogen would be sufficient?

If you don’t control the fusarium from time to time, the tomato plants will look great but give no yield. One of the other commenters mentions a new technique for winter cover crop to avoid rotation. I’m not really sure how much of a risk fusarium is for a home garden, it might be as much as our farm or perhaps minimal.

Nitrogen is necessary for proteins so you can get larger yields, but if some other nutrient is missing then nitrogen alone won’t help. K and P also need to be present in good quantities, as well as a mixture of iirc 17 elemental trace elements. I’d use a well-rounded fertilizer like 7-7-7, and if it wasn’t growing then assume there was a disease or pest at play.

This! We have the same problem.

Thank you very much.