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, for example, a back garden, littered with toys with half of it missing. Creating the details to fill the gap would be a nightmare. This suggestion is for 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 it is 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 them replaced on clean or colourful backgrounds. This takes the image out of context and removes its place in time. Keeping the restoration as historically correct, as much as possible, is my suggestion.
It is best to take the approach of repairing the scratches, and tears, correcting the fading and stains. When complete if it still looks a mess, it is 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. The photo 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.