When you edit photos in Photos using the Edit view, you have to click the "Done" button, when you have applied all adjustment. Then the photo should appear with the adjustments applied. There is no "Save" button.
Or are you editing photos with an external editor? And are calling the editor from Photos with "Image > Edit with ..."? It will depend on the editor you are using, if the edits can be saved back to Photos. Which editor are you using?
If the editor is not fully compatible with Photos and cannot be updated, you may want to save the edits with "Save as ...", so you can find the edited version in folder in the Finder.
Then import the edited photo to Photos.
I am using the External Editors extension to pair the saved, edited photo with the original in Photos. "External Editors" offers a very useful command "replace file". I simply select the photo I have yjust edited, then click Edit, call the External Editors extension, click "replace file" and select the saved, edited image as a replacement. The extension will pair it with the original.