on balance, I think you should have some suspension to help with your shoulder injury.
It's true that cheap steel coil forks don't compare against high end air forks but they are not usually aimed at the same application.
In your specific case, a good suspension post such as the Suntour SP12-NCX may just do the job but it does not work the same way a suspension fork does.
You body moves backward when you hit a bump.
Adding a coil fork like Suntour NEX that you see on zillions of e-bikes does not cost much and the additional comfort that you get for your wrists and shoulders easily justify the expense. For ebikes, the additional weight is not a problem.
Also in most cases, the Suntour NEX does the job reasonably well, you can always replace it with a better one later.
www.srsuntour.com