Nope, no screen protector.
If at some point you do buy a new iPad, make sure you get at least the 2nd pencil generation. It is much better, as
1) it has a magnet and sticks to the side of the iPad
2) It charges when attached on the side of the iPad (with the said magnet), instead of you having to stick the pencil in the iPad’s charging connector (giving the ridiculous look you saw the other day).
The soft end of this works for me :
6in1 Tech-Tool Pen, Ballpoint Pen/Touch Screen Stylus/Flat-Head and Phillips Screwdriver/Ruler/Spirit Level, Multifunction Tool for Mens, Yellow https://www.amazon.co.uk/dp/B07476LLTZ/ref=cm_sw_r_cp_tai_6avADbX1SMSPJ
This is another one I bought at some point, never used, but it works
The tip is a soft/springy metallic soft of material.