Hi PennyFarthing.
As a back sufferer since 1983, may I suggest you don't get too hung up on the handlebar style. I now have to endure spinal stenosis symptoms resulting from that original injury in addition to the more common complaints of lumbago & sciatica.
In my experience, if you opt for the retro style bars, you will become uncomfortable in that upright riding position fairly quickly, (after just a few miles or anything further than the local shop) and will end up adjusting the bars till your posture is in a similar position to that afforded by straight bars. That position is not dissimilar to riding with drop handlebars but hands on top.
If you ever observe people using zimmer frames, you will notice that they quite often lean forward for long periods rather than stand straight up. The reason for that is quite simply that the leaning forward position is actually less stressful on the lower back than the straight up approach. Having ridden quite a few miles using different bar types, I can testify that leaning slightly forward is easier on my back although that too can become painful after a bit and I vary things by sitting up straight and pedalling easily for a spell.
If some medical type has suggested to you that sitting up straight while cycling is good for the back, then I'd find myself another medic if I were you. The pressure on the facet joints is eased by leaning forward and they are under greater compression when the spine is erect.
While it's rare for people suffering from lower back disc/nerve impingement syndrome to present with exactly the same symptoms, standing ramrod straight, although desirable in guardsmen, is not conducive to a pain-free, supple back. It may be good to stand straight for some exercises to strengthen the back but for a damaged back, it's not so clever.
The eternal advice to prospective ebike owners that one should test-ride as many different types as possible holds good, particularly so for back sufferers. I'm sure there must be plenty of back sufferers amongst forum members but I'm fairly confident that not many would wish to ride significant distances in the manner that we see on film clips of pretty young things flitting around Amsterdam.
I have bikes with straight bars and another with the retro-style bars you mention and I can get along fine with both types so my advice is simply that you shouldn't pass up some of the very decent ebikes out there, simply on account of the handlebar style.
A decent saddle and suspended seat post is worthwhile in addition to good quality suspended front forks unless you're intending to do any road racing.
Regards,
Indalo