When restoring a photo it’s often the background will be damaged. To keep the restore authentic, it’s best to restore the background rather than replace it. It would be very tempting to replace it as it would be the easy route.
I appreciate some backgrounds may be a bit challenging, say of a back garden, littered with toys and be half missing so recreating them would be a nightmare. This suggestion is for the more simple backgrounds. The plainer ones or the less complicated. Postcard portraits have them, old board based photos have them, simple studio photos have them.
I am not a fan of changing the background. It always looks out of place and unnatural especially if its done with filters created from clouds and then over smoothed without matching the grain or naturally occurring texture of the original photo.
My proposal is to keep history as it was. Genealogists have nightmares about images that have been changed around. Eastern countries have a trend to cut out figures and have the replaced on clean or colourful backgrounds. This takes the image out of context and removes its place in time. Keeping the restore historically correct as much as possible. I cant lecture my customers on the importance of keeping the background as it but I can try.
Its best to take the approach of repairing the scratches, and tears, correcting the fading and stains. When complete if it still looks a mess, its worth experimenting with the dust and scratches filter to even out the tones in the background. It may then take a bit of work to even out the textures with the patch and clone tools and create a complete background without actually replacing it. It may need some texture or grain matching at this final stage. The background should now be much more convincing than if it was simply filtered to produce some random, over smoothed clouds.