I tore the posterior horn of the medial meniscus (most common tear site) in my left knee about 5 years ago (confirmed by MRI). I did not have surgery, so my experience may not be as relevant, but there are things in common. Knee was painful and I limped for several months, but it gradually recovered to almost normal. I continued all activities, even while limping.
A couple months ago, I di a little too much fast running and progressed the tear a little further (it's not as bad this time, only maybe 30% as bad as the original problem). Knowing exactly what it was, this time I did not bother with the Doc, but just continued my normal activities. It's improving quickly, and I think it will be back to normal again in another month or so.
Some things I have learned during this, from study and from my own actions and symptoms (obviously, each individual is different, I am not a doc, and YMMV):
>What causes the prompt syptoms of the torn meniscus is rough edges and flaps on the tear, that irritate the surrounding tissue.
>The surgery (at least in adults) cannot repair the meniscus. What they are doing is removing material that has rough edges. This is why the surgery works to relieve symptoms. (As an aside, I believe I accomplished the same thing over a longer period of time by continuing my normal activities. Rough edges were worn smooth anatomically.)
>Historically (1960s) the entire meniscus would be removed in open surgery. (Docs didn't know what the meniscus was for, so the prevailing thought was that it was just "extra cartilage" and it was removed like tonsils or the appendix!) This resulted in a "bone on bone" condition, and subsequent knee failure. Based on this, I think today as little as possible is removed.
>So unless a lot of meniscus has been removed, residual pain during the long recovery is probably not due to "lack of padding" inside the knee, but rather to the fact that the surgical procedure is imperfect in removing all the rough edges, and due to the long term irritability of the surrounding tissue.
>It's important to differentiate more "closed chain" from more "open chain" activities. In a closed chain activity, there is constant resistance (like standing and squatting). This keeps the knee joint approximated. In an open chain activity, resistance is interrupted (as in running). This allows the knee to "hang free" in space, and allows the joint to be in traction.
>For my own recent re-injury, I observed that long hikes with a heavy pack caused no problem, but even a very short few strides of running caused immediate pain. Many people believe this is because of "impact." But given everything above, I do not think impact is the villain here. I think what happens is that is the activity has a long enough open chain period, the rough edges on the tear lift up, and it hurts to push them back down. In a more closed activity, like walking even with a heavy pack, the tear is kept compressed, and this doesn't happen. I was able to confirm this in myself by running while isometrically contracting my quad and hamstring in the injured leg. Doing this, I ran pain free, because the joint was kept compressed. Of course this is exhausting and impractical for anything other than a very short distance, but it confirmed my thinking.
What made me post all this was your observation that hiking seems to be OK, but even a little running hurts a lot. You may find that hiking, even long rough hikes and heavy packs, will become just fine, but running and jumping type activities will take a LOT longer to become pain free. I did the Great Range (ADKs) last weekend pain free, but if I were to run across the parking lot to my car (without thinking to use the "artificial gait" described above) it would hurt a lot.
Depending on the location of your injury, another thing that may help will be stretching and massage to keep muscles warm and loose. In particular, I have to work constantly on my popliteus muscle. This is a small muscle in the back of the thigh that participates in starting knee flexion when the knee is near full extension. Interestingly, one head of the popliteus actually attaches to the posterior horn of the medial mensicus. So when the knee hurts, the popliteus wants to spasm to try to protect the knee from hyperextension; it pulls on the mensicus; and the knee hurts more (classic "pain-spasm-pain" cycle).
Good luck with your continued recovery!