The approach this time was:

1. iterate through the characters to find a * symbol
2. Search the characters around it for a digit.
3. Get the value of the number associated with that digit by searching backwards until you find the start of a number
4. Use union-find to track whether or not you've seen this number before (because you can't assume that the same value is the same number)

A simpler approach would consider that you only have two numbers on the same line for the same gear if the character in the gear column is a non-digit; otherwise, if a number is adjacent to a gear, there is only one on that row. Union-find is completely overkill, but I like using it even when I don't need to.

Anyway, upon reflecting on this, while the general approach is fine, I didn't think too hard about the implementation and just ended up with globs of overly memoized spaghetti. I probably should check if Dart has a python-like tuple object or similar. Whatever. Behold!

void day3s() {
  List lines = [
    for (String? line = stdin.readLineSync();
        line != null;
        line = stdin.readLineSync())
      line
  ];

  List> digs = [for (int i = 0; i < lines.length; i++) Map()];
  int? isDigitMem(int r, int c) {
    return digs[r].putIfAbsent(c, () => isDigit(lines[r][c]));
  }

  // first entry is parentc, second is size
  List>> uf = List.generate(
      lines.length, (i) => List.generate(lines[0].length, (j) => [j, 1, -1]));

  int find(int r, int c) {
    if (uf[r][c][0] != c) {
      uf[r][c][0] = find(r, uf[r][c][0]);
      return uf[r][c][0];
    }
    return uf[r][c][0];
  }

  void union(int r, int cp, int c) {
    cp = find(r, cp);
    c = find(r, c);

    if (c == cp) {
      return;
    }

    if (uf[r][cp][1] >= uf[r][c][1]) {
      uf[r][c][0] = cp;
      uf[r][cp][1] += uf[r][c][1];
    } else {
      uf[r][cp][0] = c;
      uf[r][c][1] += uf[r][cp][1];
    }
  }

  int stoi(int row, int col) {
    int acc = 0;
    for (int i = col; i < lines[0].length; i++) {
      int? d = isDigitMem(row, i);
      if (d != null) {
        acc = (acc * 10) + d;
        union(row, col, i);
      } else {
        break;
      }
    }
    return acc;
  }

  int? stoiSearch(int row, int col) {
    assert(row >= 0 && col >= 0 && row < lines.length && col < lines[0].length);
    if (isDigitMem(row, col) == null) {
      return null;
    }
    int i = col - 1;
    while (i >= 0) {
      if (isDigitMem(row, i) == null) {
        return stoi(row, i + 1);
      }
      i--;
    }
    return stoi(row, 0);
  }

  List> s2i = [for (int i = 0; i < lines.length; i++) Map()];
  int? stoiSearchMem(int row, int col) {
    return s2i[row].putIfAbsent(col, () => stoiSearch(row, col));
  }

  int count = 0;
  for (int i = 0; i < lines.length; i++) {
    for (int j = 0; j < lines[0].length; j++) {
      if (lines[i][j] != "*") {
        continue;
      }

      List gearVals = List.empty(growable: true);
      for (int x = -1; x <= 1; x++) {
        if (i + x < 0 || i + x > lines.length) {
          continue;
        }

        Set parents = {};
        for (int y = -1; y <= 1; y++) {
          if (j + y < 0 || j + y > lines[0].length) {
            continue;
          }

          int? cur = stoiSearchMem(i + x, j + y);

          int parent = find(i + x, j + y);
          if (parents.contains(parent)) {
            continue;
          }

          parents.add(parent);

          if (cur != null) {
            gearVals.add(cur);
          }
        }
      }

      if (gearVals.length == 2) {
        count += gearVals[0] * gearVals[1];
      }
    }
  }

  print(count);
}