I’d imagine the limiting factor in all of these is still functionality of these organs. We can reorganize them to look somewhat like the actual organ (like in the linked article), but whether or not the organ functions the same is still under much investigation.

Also how do you connect up the nerves? A heart transplant works because the heart is basically self-regulating. But the eye needs thousands of nerves to connect to the brain to be useful.

Just grow nerves to the stem of the brain. Axons could do it, they did for everyone who was born with healthy eyes.

It would be quite an achievement though, because axons navigate their way by a gradients of some chemicals, which probably dissipate with age.

And problems will not end when nerves have grown. Brains would need to learn how to use them.

"Just"

I mean, that it doesn't matter how many axons are there, because no one is going to lay them one-by-one.

this word does a lot of work, it seems

This is weird because the vagus nerve and breathing rate can both slow/speed up the heart. What about when doing exercise, how is the signal sent to the heart to say speed up?

Cutting edge work in bioelectrical fields (see Michael Levin's lab) looks quite promising, although quite a long way off in terms of human applications. They can do all sorts of seemingly miraculous things in planaria.

Levin gave a mind boggling talk about some of their work a couple years ago: https://youtu.be/RjD1aLm4Thg