Nim

Runtime: ~~7ms~~ 3.18 ms

Part 1: I use flood fill to count all grouped plants and keep track of each border I see.
Part 2: I use an algorithm ~~similar to "merge overlapping ranges"~~ to count spans of borders (border orientation matters) in each row and column, for each group. Resulting code (hidden under spoiler) is a little messy and not very DRY (it's completely soaked).

Edit: refactored solution, removed some very stupid code.

proc groupSpans(borders: seq[(Vec2, Dir)]): int =
  ## returns number of continuous groups of cells with same Direction
  ## and on the same row or column
  var borders = borders
  var horiz = borders.filterIt(it[1] in {U, D})
  while horiz.len > 0:
    var sameYandDir = @[horiz.pop()]
    var curY = sameYandDir[^1][0].y
    var curDir = sameYandDir[^1][1]
    for i in countDown(horiz.high, 0):
      if horiz[i][0].y == curY and horiz[i][1] == curDir:
        sameYandDir.add horiz[i]
        horiz.del i
    sameYandDir.sort((a,b)=>cmp(a[0].x, b[0].x), Descending)

    var cnt = 1
    for i, (p,d) in sameYandDir.toOpenArray(1, sameYandDir.high):
      if sameYandDir[i][0].x - p.x  != 1: inc cnt
    result += cnt

  var vert = borders.filterIt(it[1] in {L, R})
  while vert.len > 0:
    var sameXandDir = @[vert.pop()]
    var curX = sameXandDir[^1][0].x
    var curDir = sameXandDir[^1][1]
    for i in countDown(vert.high, 0):
      if vert[i][0].x == curX and vert[i][1] == curDir:
        sameXandDir.add vert[i]
        vert.del i
    sameXandDir.sort((a,b)=>cmp(a[0].y, b[0].y), Descending)

    var cnt = 1
    for i, (p,d) in sameXandDir.toOpenArray(1, sameXandDir.high):
      if sameXandDir[i][0].y - p.y  != 1: inc cnt
    result += cnt

type
  Dir = enum L,R,U,D
  Vec2 = tuple[x,y: int]
  GroupData = object
    plantCount: int
    borders: seq[(Vec2, Dir)]

const Adjacent: array[4, Vec2] = [(-1,0),(1,0),(0,-1),(0,1)]

proc solve(input: string): AOCSolution[int, int] =
  let grid = input.splitLines()
  var visited = newSeqWith(grid.len, newSeq[bool](grid[0].len))
  var groups: seq[GroupData]

  proc floodFill(pos: Vec2, plant: char, groupId: int) =
    visited[pos.y][pos.x] = true
    inc groups[groupId].plantCount
    for di, d in Adjacent:
      let pd: Vec2 = (pos.x+d.x, pos.y+d.y)
      if pd.x < 0 or pd.y < 0 or pd.x > grid[0].high or pd.y > grid.high or
        grid[pd.y][pd.x] != plant:
        groups[groupId].borders.add (pd, Dir(di))
        continue
      if visited[pd.y][pd.x]: continue
      floodFill(pd, plant, groupId)

  for y in 0..grid.high:
    for x in 0..grid[0].high:
      if visited[y][x]: continue
      groups.add GroupData()
      floodFill((x,y), grid[y][x], groups.high)

  for gid, group in groups:
    result.part1 += group.plantCount * group.borders.len
    result.part2 += group.plantCount * group.borders.groupSpans()

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