Adding image to same slot for backed sdata

When writing an image to zarr with overwrite=True, I found some unexpected behaviour.
Below I give a mimimal example to reproduce the issue.

This works, as expected. I can overwrite image layer 'image'.

import spatialdata
import numpy as np

sdata = spatialdata.SpatialData()

sdata.write( 'sdata.zarr' )

arr=np.random.rand( 1,100,100 )

spatialelement=spatialdata.models.Image2DModel.parse(
            arr, dims=[ 'c' ,'y', 'x' ],
        )

sdata.add_image( name="image", image=spatialelement , overwrite=True )

sdata.add_image( name="image", image=spatialelement , overwrite=True )

However, when I add some processing (e.g. multiplying by two) before replacing sdata["image" ]:

spatialelement=spatialdata.models.Image2DModel.parse(
            sdata[ "image" ].data*2, dims=[ 'c' ,'y', 'x' ],
        )

sdata.add_image( name="image", image=spatialelement , overwrite=True )

I get the error:

ValueError Traceback (most recent call last)
in SpatialData.add_image(self, name, image, storage_options, overwrite)
659 target_path = os.path.realpath(os.path.join(self.path, "images", name))
660 if target_path in files:
--> 661 raise ValueError(
662 "Cannot add the image to the SpatialData object because it would overwrite an element that it is"
663 "using for backing. See more here: https://github.com/scverse/spatialdata/pull/138"
664 )
665 self._add_image_in_memory(name=name, image=image, overwrite=overwrite)
666 # old code to support overwriting the backing file
667 # with tempfile.TemporaryDirectory() as tmpdir:
668 # store = parse_url(Path(tmpdir) / "data.zarr", mode="w").store
(...)
692 # image = _read_multiscale(str(tgt_element_path), raster_type="image")
693 # self._add_image_in_memory(name=name, image=image, overwrite=True)

ValueError: Cannot add the image to the SpatialData object because it would overwrite an element that it isusing for backing. See more here: https://github.com/scverse/spatialdata/pull/138

However, if I do a persist(), I am allowed to overwrite:

spatialelement=spatialdata.models.Image2DModel.parse(
            (sdata[ "image" ].data*2).persist(), dims=[ 'c' ,'y', 'x' ],
        )

sdata.add_image( name="image", image=spatialelement , overwrite=True )

And I am also allowed to do this (typical scenario where you want to do some processing twice with e.g. different parameters etc.):

spatialelement=spatialdata.models.Image2DModel.parse(
            sdata[ "image" ].data*2, dims=[ 'c' ,'y', 'x' ],
        )

sdata.add_image( name="image2", image=spatialelement , overwrite=True )

spatialelement=spatialdata.models.Image2DModel.parse(
            sdata[ "image" ].data*2, dims=[ 'c' ,'y', 'x' ],
        )

sdata.add_image( name="image2", image=spatialelement , overwrite=True )

Start at SpatialData.add_image, especially the backing-file check around the reported traceback, and reproduce the issue with the minimal examples in the report. Compare lazy data from sdata["image"].data with the persisted result and the image2 case. Done means the intended overwrite behavior is established and covered by a regression test.