Is it possible to see the stars from LR or Bridge in Photoshop CC 2021 dialog box?

I presume that you are referring to the File/Open dialog?

Scripting could offer some possibilities beyond the basic open dialog. That is the whole reason for Bridge, which started life as an integrated file browser inside Photoshop before being split off as a separate program.

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@mal25 wrote:

Is it possible to see the stars given in LR or Bride in the Photoshop

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Yes. In Photoshop, choose File > File Info to see metadata that Bridge, Lightroom, or other applications have saved in that document (or in its XMP sidecar file, if it was a camera raw file). In the figure below, the 3-star rating was applied in Bridge, and it’s visible after opening the image in Photoshop. If you change any of this metadata in Photoshop and save the document, you’ll see the change in Bridge.

However, there is no way to see the rating information in Photoshop when that dialog box is not open.

That same File > File Info dialog box is available in other Adobe applications such as Illustrator, InDesign, and also Bridge.

Since you mentioned Lightroom, if you’re using Lightroom Classic, it doesn’t save the rating to the file until you choose Metadata > Save Metadata To File (Library module) or Photo > Save Metadata To File (Develop module). And Lightroom Classic won’t pick up metadata changes made in other applications unless you choose Read Metadata from File from the same menus. Bridge works differently; it always writes out metadata changes as soon as you change them, and immediately notices external changes as soon as another application updates the file.