There is no Apple-like, smart Bluetooth stylii available for an over 9-year old 2012 iPad 3rd generation.
That stated, there are plenty of commonplace, find anywhere, capacitive stylii that pretty much still work like using your finger.
The better of the commonplace, find anywhere capacitive stylii are clear disc stylii that allow you to see the exact area the stylus will mark at.
These are very good for precision sketching/drawing and writing and are much better than the fat squishy tip type of commonplace capacitive stylii.
The only drawback is you must keep the disc tip of the stylus and your tablet free of dirt and grit to avoid scratching the tablet screen.
They won't have any pressure sensitivity or palm rejection, but they are stylii made to work with touch screens.
If you want a fine-point stylus, there are plenty of rechargeable battery powered, so-called “Active” fine point, capacitive stylii on the market.
These use a tiny battery to send small electrical impulses to a fine tip point of the stylus that simulates a finger touch.
Lots of these available to use with that old iPad.
Look to Amazon for these.
Tap my link below.
https://www.amazon.com/s?k=fine+point+battery+powered+capacitive+stylii&ref=nb_sb_noss
Same previous precautions, I mentioned apply.
These types of stylii work with any tablet or smart phone.
To combat the NO palm rejection issue with such capacitive stylii, you can use special, non-body electrical conducting, lycra-based material drawing glove that works by isolating your hand/palm and allow you to lay your hand/palm on the screen as you draw in these non-compatible Adonit stylus apps.
Something like these found on Amazon.
https://www.amazon.com/AKX-Rejection-Drawing-Graphic-Sketching/dp/B08R6PWKC9/ref=sr_1_33_sspa?dchild=1&keywords=tablet+drawing+gloves&qid=1611535160&sr=8-33-spons&psc=1&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUExMFg5WFBZWFpCS1kmZW5jcnlwdGVkSWQ9QTA5OTA2MzMxRUVYUURUMlAwVU4wJmVuY3J5cHRlZEFkSWQ9QTAxNDY1NjMxVjg1NE45TVRXSUQ3JndpZGdldE5hbWU9c3BfYXRmX25leHQmYWN0aW9uPWNsaWNrUmVkaXJlY3QmZG9Ob3RMb2dDbGljaz10cnVl
https://www.amazon.com/Timebetter-Rejection-Drawing-Sketching-Suitable/dp/B08DKGHYMS/ref=sr_1_21?dchild=1&keywords=drawing+gloves&qid=1611533128&sr=8-21
Many more makers of these types of gloves found on Amazon and in different hand sizes, as well!
Good Luck!