If your Schedule K-1 has capital gains, the amount will be reported on Schedule D.
K-1s have boxes for net short-term and net long-term capital gains. Those amounts will transfer to Schedule D lines 5 and 12.
I do see Long Term gain but then I see in line 10 a positive dollar amount, line 12, a negative dollar amount, and in line 13 a capital gain distribution (positive) amount. This is the part I do not understand. Is the LTCG rate the same and with any investment based on income level?
The amount on line 13 is unlikely to have come from the K-1. Check for a 1099-DIV with an amount in box 2a.
Otherwise, review the K-1 and your K-1 entries to see where the Capital gains distribution amount came from.