With two pair plus a flush draw and getting 3:1, folding river versus a small block bet is too conservative.
Flop 7s8cJc is very dynamic and connected; with AKo we have overcards plus a backdoor nut flush draw, so a small c-bet works well as a semi-bluff. Betting about one-third pot pressures SB’s weaker pairs and draws while keeping our range protected.
Turn 7c pairs the board and gives us a flush draw; SB’s range is now weighted toward Jx/8x/7x and some draws, while we still have strong overcards and a draw. Solver leans toward checking here, but a big barrel is also reasonable. Checking keeps our range flexible and avoids overplaying a hand that’s still strong but not yet made.
River 8d puts the board 7s8cJc7c8d, and SB now has ~11.7BB behind and bets 4BB into 11.9BB, giving us ~3:1 and needing ~25% equity. Our hand is now two pair (A-high, K-high) and we still hold a flush draw, so we have plenty of equity versus a range that can contain missed draws, Jx/8x/7x, and some bluffs. Calling is preferred; folding is too tight.
Note: Folding river versus a small block bet with two pair plus a flush draw and getting ~3:1 is too conservative; calling is the higher-EV option.