Home DIY

You're on the right track but you still have to really properly even out the damaged area and once you've done that you might just skip the extra lining. Most lining makes any damage underneath stand out rather than covering it up. An alternative is stripping that part of the wall and starting from scratch but them you will need to resurface all the areas you damage removing the paper.

Wait until everything is fully dry first. I find this gives me an opportunity to delay the job for a very long time ! :) Then use border adhesive to stick the original lining back down, use a string to get under it if necessary. It won't go back perfectly but you can use a seam roller or trim it if it wants to overlap in places but really that should all go back pretty neatly. Keep the surface bvery clean of paste washing with clean water regularly.

Then apply TX110 or similar filler, and sponge the excess off once it drys, don't leave it weeks though, let it dry overnight and then use a sponge to wipe the excess, very lightly with some sandpaper if you must but finish with the sponge, feather around the areas so there are no edges. Paint the filler and surrounding area with Gardz, don't miss this step because your filler will show under the emulsion if you do.

Now you can line or paint. Personally I'd paint first and it would probably be fine, there may be aspects I can't see from the photos that would be difficult but that would be my approach.