C#

There is probably a more efficient way of finding the sides, but this way was what came to me.

using System.Diagnostics;
using Common;

namespace Day12;

static class Program
{
    static void Main()
    {
        var start = Stopwatch.GetTimestamp();

        var sampleInput = Input.ParseInput("sample.txt");
        var programInput = Input.ParseInput("input.txt");

        var (samplePart1, samplePart2) = Solve(sampleInput);
        Console.WriteLine($"Part 1 sample: {samplePart1}");
        Console.WriteLine($"Part 1 input: {samplePart2}");

        var (inputPart1, inputPart2) = Solve(programInput);
        Console.WriteLine($"Part 2 sample: {inputPart1}");
        Console.WriteLine($"Part 2 input: {inputPart2}");

        Console.WriteLine($"That took about {Stopwatch.GetElapsedTime(start)}");
    }

    static (int part1, int part2) Solve(Input i)
    {
        var retail = 0;
        var bulk = 0;
        var allPlotPoints = new Dictionary<char, HashSet<Point>>();
        foreach (var p in Grid.EnumerateAllPoints(i.Bounds))
        {
            var plant = i.ElementAt(p);

            if (!allPlotPoints.TryGetValue(plant, out var previousPlotPoints))
            {
                previousPlotPoints = new();
                allPlotPoints[plant] = previousPlotPoints;
            }
            else if (previousPlotPoints.Contains(p)) continue;

            var plotPoints = new HashSet<Point>();
            var perimeter = SearchPlot(i, plotPoints, plant, p);
            var area = plotPoints.Count;
            var sides = CountSides(plotPoints);
            retail += area * perimeter;
            bulk += area * sides;

            previousPlotPoints.AddRange(plotPoints);
        }

        return (retail, bulk);
    }

    static int CountSides(HashSet<Point> plot)
    {
        var sides = 0;

        // Track the points we've visited searching for sides
        HashSet<Point> visitedDownRight = new(),
            visitedDownLeft = new(),
            visitedRightDown = new(),
            visitedRightUp = new();

        // Sort the points in the plot from upper-left to lower-right, so we can
        // go through them in reading order
        foreach (var p in plot.OrderBy(p => (p.Row * 10000) + p.Col))
        {
            // Move right while looking up
            sides += GetSideLength(p, plot, visitedRightUp, Direction.Right, Direction.Up) > 0 ? 1 : 0;
            
            // Move right while looking down
            sides += GetSideLength(p, plot, visitedRightDown, Direction.Right, Direction.Down) > 0 ? 1 : 0;
            
            // Move down while looking right
            sides += GetSideLength(p, plot, visitedDownRight, Direction.Down, Direction.Right) > 0 ? 1 : 0;
            
            // Move down while looking left
            sides += GetSideLength(p, plot, visitedDownLeft, Direction.Down, Direction.Left) > 0 ? 1 : 0;
        }

        return sides;
    }

    static int GetSideLength(Point p, HashSet<Point> plotPoints, HashSet<Point> visited, Direction move, Direction look)
    {
        if (!plotPoints.Contains(p)) return 0;
        if (!visited.Add(p)) return 0;
        if (plotPoints.Contains(p.Move(look))) return 0;
        return 1 + GetSideLength(p.Move(move), plotPoints, visited, move, look);
    }

    static int SearchPlot(Input i, HashSet<Point> plotPoints, char plant, Point p)
    {
        if (!plotPoints.Add(p)) return 0;
        return p
            .GetCardinalMoves()
            .Select(move =>
            {
                if (!i.IsInBounds(move) || (i.ElementAt(move) != plant)) return 1;
                return SearchPlot(i, plotPoints, plant, move);
            })
            .Sum();
    }
}

public class Input
{
    public required string[] Map { get; init; }
    
    public Point Bounds => new Point(this.Map.Length, this.Map[0].Length);
    public char ElementAt(Point p) => this.Map[p.Row][p.Col];
    public bool IsInBounds(Point p) => p.IsInBounds(this.Map.Length, this.Map[0].Length);
    
    public static Input ParseInput(string file) => new Input()
    {
        Map = File.ReadAllLines(file),
    };
}