Urgent referrals are pretty common from opticians in my experience, I’ve been referred on many many occasions and it’s always urgent, always handled quickly and always not an emergency. I do have problems with my eyes but nothing urgent.
The reason they err towards urgency is because eyes can signal problems elsewhere so they like to check anything they find quickly in case other referrals are needed.
Specifically on the peripheral vision part of your question, I have severely reduced peripheral vision in my right eye, if you saw the results sheets it is displayed as a circle and every light missed is shown as a black dot on the circle. My results look like the image attached. The cause in my case is an optic disc colaboma, which is basically a small patch on the optic disc near the optic nerve that never fully formed so it’s like a hole. For me that means that over years fluid would build and recede behind the macula causing damage. It freaked out opticians because it’s a reasonably rare set of circumstances, so every new optician would look, call in students and colleagues to look and write me a referral for a new random condition. I had MRIs, photos with contrast, electroretinagrams (sp??) and every type of eye test they could think of. Ultimately it was a watch and wait situation until eventually in my 30s I ended up with a detached retina and they went in and did keyhole surgery to fix it.
I do have reduced vision in that eye, but it has no impact on my life except that I’m not allowed contact lenses because no one wants to risk me getting an infection in the good eye and losing that vision. I use computers all the time, can drive, have never found a single activity I can’t do with my current level of eyesight, but then I don’t want to be a pilot or join the military or anything, they might have issues with it I suppose.
So upshot from me is that, I understand why you are concerned, but try really hard if you can to put worry aside, just let the appointments play out and see how it goes. If there’s something to worry about they’ll let you know fast.