Dart

Suspiciously easy, so let's see how tomorrow goes.... (edit: forgot to put the language! Dart for now, thinking about Uiua later)

import 'package:more/more.dart';

var ops = [(a, b) => a + b, (a, b) => a * b, (a, b) => int.parse('$a$b')];

bool canMake(int target, List<int> ns, int sofar, dynamic ops) {
  if (ns.isEmpty) return target == sofar;
  for (var op in ops) {
    if (canMake(target, ns.sublist(1), op(sofar, ns.first), ops)) return true;
  }
  return false;
}

solve(List<String> lines, dynamic ops) {
  var sum = 0;
  for (var line in lines.map((e) => e.split(' '))) {
    var target = int.parse(line.first.skipLast(1));
    var ns = line.skip(1).map(int.parse).toList();
    sum += (canMake(target, ns.sublist(1), ns.first, ops)) ? target : 0;
  }
  return sum;
}

part1(List<String> lines) => solve(lines, ops.sublist(0, 2));
part2(List<String> lines) => solve(lines, ops);