Always good to get miles on a bike.
Most shifter housing made in the last decade or two is a plastic sleeve on the inside, a series of metal strands in the middle, and a plastic shell on the outside. You can see a cross section of your housing here:
Source, scroll down to LEX at the very bottom:
https://jagwire.com/guides/housing
In this case the inner and outer layers of the portion outside the steel strands may not be distinguishable, but that doesn't really matter. You want all of the portions of this to end at one point (ie, where you cut it). You don't want the wires sticking out farther than the liner or outer housing material like in the picture above.
It sounds like you're already doing so, but do get that front brake back into service as soon as is practical. You can stop much faster in an emergency (or any other time) with your front brake than with your rear. In the event of a sudden tube/tire blowout it's also nicer to do the braking on the wheel that's still fully functional. If you ride in inclement weather it may be worth paying the extra $ or two to get a stainless rather than normal fastener so that rust is less of an issue.
Since you seem to be soaking up all of our advice, I'll point out that your front wheel (or at least the quick release skewer) is on backwards. Does it really matter? No, not really, but convention is to put the front QR lever on the same side of the bike (left, non-drive) as the rear QR lever. The rear needs to be there so it stays out of the way of the derailer and one might as well make the front match. It is slightly helpful as many bicycle tires have a directional tread. Rather than looking for the rotation direction label when you put your front wheel back on you can just put the QR lever to the left and know all is right. Does tread direction matter? I don't know, but in cases where the manufacturer took the trouble of putting a label on, I try to follow it.
As one final note, I want to know what Shimano made those yellow chainring Biopace stickers from (material, adhesive, and ink). I understand the surviving ones have all had a gentle life, but for being 30 years old, every one I see on a bike seems to be in really good condition.