How to make small polygons from shapefile and extract coordinates

I have a small shapefile here: https://login.filesanywhere.com/fs/v.aspx?v=8c6d62865c626fb4a2ab called bay.RDS

 library(tmap)
 library(leaflet)
 library(mapview)
 bay <- readRDS('bay.RDS')
 mapview(bay)

I am trying to draw 50 meter wide polygons from shore to shore right at the below point and extract coordinates from it. I need multiple polygons next to each other but independently drawn as I need to color code them based on a column of values

pt <- st_sfc(st_point(c(-122.91, 38.17)), crs=4326)
mapview(bay) + mapview(pt, color ='red')

I have included a snapshot below of what I am trying to accomplish. I would appreciate it if someone can show me how I can make just a couple of polygons and extract the coordinates from it so I can merge them to my dataset. Let me know if is not clear

One approach, using {sf} and {dplyr}:

edit this solution was substantially rewritten following the helpful comments by @Chris and @Salvador.

TLDR: below solution creates a horizontal baseline, buffers this baseline to result in a horizontal strip of chosen width, creates adjacent clones of this strip, combines them into a multipolygon, and rotates and shifts the mulitpolygon to expand southwards from a chosen anchor.

1. helper function get_strips(...) to return a multipolygon of adjacent strips:

get_strips <- function(n = 10, ## number of adjacent strips
                       strip_width = 1e3, # unit: m
                       strip_length = 1e5,
                       crs = 3857 ## default: 'google' mercator
                       ){
  ## make horizontal line of length 'strip_length':
  baseline <- matrix(c(-strip_length/2, strip_length/2, 0, 0), ncol = 2) |>
    st_linestring()
  ## make line a polygon of width 'strip_width'
  basestrip  <- baseline |> 
    st_buffer(strip_width/2, endCapStyle = 'FLAT')
  ## return a spatial dataframe of n adjacent strips from north to south:
  st_sf(strip_id = sprintf('strip_%02.f', 1:n),
        geometry = Map(1:n,
                       f = \(index) basestrip - c(0, index * strip_width - strip_width/2)
                       )|>
          st_sfc() |> st_cast('MULTIPOLYGON') |> st_set_crs(crs)
        )
}

2. helper function to rotate the geometry of a spatial dataframe

    rotate_feature <- function(feature,
                               angle = 0, ## rotation in degree
                               anchor = c(0, 0) ## top center point of grid
                               ){
      crs <- st_crs(feature)
      a <- -pi * angle/180 ## convert to radiant ccw
      ## create rotation matrix:
      rotmat <- matrix(c(cos(a), sin(a), -sin(a), cos(a)), 2, 2)
      ## rotate, recenter, restore CRS:
      st_geometry(feature) <- st_geometry(feature) * rotmat + anchor
      feature |> st_set_crs(crs)
    }

3. load libraries, create play data

    library(sf)
    library(dplyr)
    
    the_lake <- readRDS(file.choose()) ## spatial feature supplied by OP
    the_anchor <- c(5.08e5, 4.224e6) ## anchor strip grid here

4. generate desired spatial features

    the_strips <- 
      get_strips(crs = st_crs(the_lake)) |>
      rotate_feature(angle = 30, anchor = the_anchor)
    
    the_cropped_strips <- the_strips |>
      st_intersection(the_lake)
    
    ## casting polygons to multilinestrings to only
    ## obtain the corner points (not areas) on intersection:
    the_corners <- 
      st_intersection(
        st_cast(the_strips, 'MULTILINESTRING'),
        st_cast(the_lake, 'MULTILINESTRING')
      )

5. inspect

    library(ggplot2)
    
    anchor_point <- the_anchor |> st_point() |>
                                  st_sfc(crs = st_crs(the_lake))
    
    ggplot() +
      geom_sf(data = the_lake) +
      geom_sf(data = the_strips, fill = NA) +
      geom_sf(data = the_cropped_strips, aes(fill = strip_id)) +
      geom_sf(data = the_corners) +
      geom_sf(data = anchor_point, pch = '+', size = 5) +
      geom_sf_label(data = anchor_point, nudge_y = 1e3, label = 'Anchor') +
      coord_sf(xlim = 1e5 * c(5, 5.2), ylim = 1e6 * c(4.21, 4.235))

6. extract corners per polygon:

    the_corners |>
      rowwise() |>
      reframe(strip_id,
              coords = st_coordinates(geometry)
              )

    ## # A tibble: 50 x 2
    ##    strip_id coords[,1]     [,2]  [,3]
    ##    <chr>         <dbl>    <dbl> <dbl>
    ##  1 strip_01    508864. 4223922.     1
    ##  2 strip_01    507927. 4223381.     1
    ##  3 strip_01    508230. 4222400.     1
    ##  4 strip_01    509328. 4223035.     1
    ##  5 strip_02    508230. 4222400.     1
    ##  6 strip_02    508791. 4221570.     1