Removing Wallpaper Glue – All of it or can I leave faint bits behind

You will need to take off all the glue if you want a good finish.

The paint will lift the glue, but unevenly, and mix with the paint. This will cause the paint to clump and not cover properly and all in all it will look terrible.

I know because I did this in the first house I owned and had to wash the walls of the one room where I tried this several times to get as much glue off as possible. I don't think I got it completely off and you could still tell.

If you just want to paint the room, you would be better off hanging lining paper and then painting that. This has the added advantage (especially if you use 1000gsm paper) of covering any imperfections in the wall.

I would not paper over paper. In your case there is already a big chance that you have compromised the adhesion of the existing paper to the subsurface when the ceiling was exposed to the steam. Also to be considered is that the existing paper may not be a good surface to hold wall paper glue.

So I suggest getting the steamer back and removing the old ceiling paper too. Before putting on new paper make sure to seal the wall surface properly. The staining of the previous ceiling paper due to the steam could be an indicator that previous sealing was never done or has failed with age.