Do I need to replace my apple pencil nib?

The hardness of the material chosen will be a trade-off between “feel” (a product of friction between the screen and the tip) and longevity.

Given that the unprotected iPad Pro screen has a slightly matt (non reflective) texture, the tip material reportedly provides “a paper like feel” when using the pencil. If using a screen protector, the feel will be different. A gloss finish will be a little more slippery.

I must confess, if you only use your Apple Pencil with your iPad, then I’m a little surprised that you’ve managed to wear it out quite so quickly.

My mistake. Upon checking, I note that the second-generation Apple Pencil doesn’t appear to be supplied with a spare - unlike the original Apple Pencil which is supplied with a spare pencil tip.

Either way, if metal is exposed, a replacement tip is needed. The tip provides a soft material that is intended to glide over the screen coating. Your Pencil is a precision [and relatively expensive] precision instrument - and should be treated with some care. If the tip is damaged or worn,, as with anything else that is drawn across your [very expensive] iPad screen, it has the capacity to cause damage.

I hope this has been helpful.

Yes, you need to replace the tip. In the box, in which the Pencil was supplied, you should find a spare tip - otherwise, they are available to buy.

The pencil tip is considered a consumable part - and is unlikely to be replaced for free.

I would not call them "consumable". Certainly should last longer that 3 weeks. I've been using mine for two months and it has no detectable wear. I do not use a screen protector. Do you tend to push hard on the screen? I have a tendency to push really hard when writing with pen/pencil on paper, and had to train myself to not do so on my iPad Pro. Doing so could certainly wear down the tip.

What kind of screen protector are you using? If it’s a matte finish like PaperLike, maybe it’s too toothy and wears your nib too quickly? Just a guess.