https://proj.org/en/stable/operations/projections/omerc.html
prj <- "+proj=omerc +lonc=-119 +lat_0=37 +gamma=30"
m <- do.call(cbind, maps::map("state", "california", plot = F)[1:2])
library(terra)
#> terra 1.8.50
plot(terra::project(m, to = prj, from = "EPSG:4326"), pch = ".", asp = 1/cos(37 * pi/180), type = "b")
#> Warning: [project] 3 failed transformations
## now get more serious
## devtools::install_github("ropensci/rnaturalearthhires")
cali <- terra::vect(rnaturalearth::ne_states("United States of America") |> dplyr::filter(name == "California"))
pcali <- terra::project(cali, prj)
## get some imagery
imgsrc <- "<GDAL_WMS><Service name=\"TMS\"><ServerUrl>http://services.arcgisonline.com/ArcGIS/rest/services/World_Imagery/MapServer/tile/${z}/${y}/${x}</ServerUrl></Service><DataWindow><UpperLeftX>-20037508.34</UpperLeftX><UpperLeftY>20037508.34</UpperLeftY><LowerRightX>20037508.34</LowerRightX><LowerRightY>-20037508.34</LowerRightY><TileLevel>17</TileLevel><TileCountX>1</TileCountX><TileCountY>1</TileCountY><YOrigin>top</YOrigin></DataWindow><Projection>EPSG:900913</Projection><BlockSizeX>256</BlockSizeX><BlockSizeY>256</BlockSizeY><BandsCount>3</BandsCount><MaxConnections>10</MaxConnections><Cache /><ZeroBlockHttpCodes>204,404,403</ZeroBlockHttpCodes></GDAL_WMS>"
px <- dev.size("px") ## get current plot size
ex <- par("usr") ## current plot
rr <- terra::rast(terra::ext(ex), ncols = px[1], nrows = px[2], crs = prj)
im <- terra::project(terra::rast(imgsrc), rr, by_util = TRUE, method = "cubic")
terra::plotRGB(im, add = TRUE)
plot(pcali, col = NA, border = "firebrick", lwd = 4, add = TRUE)