The 1881 and 1882 cents are extremely complicated, particularly the hybrids, and numerous hybrid dies were sunk and used. The best study of them I have seen has been done by another collector but is yet unpublished. His study was based on far more coins in hand, several hundred across both dates, than was my study in Dies & Diadems. I referred to it several times in my recent CN Journal articles. It is excellent.
Most (and perhaps all) of the obverse punches used in 1881 were raised with single serifs and the double serifs were added by re-punching the working dies individually. This re-punching by Heaton was often poorly done and remnants of the underlying single serif letters can be seen on some dies, like the one you posted.
It generally took three pressings to sink an obverse die in 1881 and 1882. Often, the same punch was not used in the three successive pressings, hence the hybrid dies. Add to that the facts that the different punches and dies distorted to varying degrees, that dies were uniquely corrected by re-punching, and you get the complicated landscape that is 1881 and 1882 cents. I would respectfully suggest you read the following two articles which describes a few fascinating 1882 obverse hybrid dies and how they came to be. The articles are also generally applicable to the die-sinking process used in 1881.
Dan Flynn and Rob Turner, "Unintended Consequences - The 1882-H Obverse 2 over 1 Cents from the Heaton Mint," Canadian Numismatic Journal, vol. 68, no. 5, (Markham ON:
RCNA, July/August 2023), 212-219.
Rob Turner, "A Numismatic Unicorn," Canadian Numismatic Journal, vol. 69, no. 8, (Markham ON:
RCNA, December 2024), 352-357.