Add the option to mark the building as abandoned
Now you can only mark it as Non-existent. In practice, buildings often stay in place for a long time and serve as a landmark, but people stop caring for them.
Other? Where is it located?
And in fact, I propose another button in addition to the already existing Does Not Exist
Details

In that picture of yours, under Building row, you can click ... and choose ruins, if that helps?
Hmm, an interesting question is which tag to use. I initially thought about the abandoned=yes tag. But it turns out that there is a similar tag disused=yes.
buildings=ruins is also suitable, however, using it we lose the former purpose of the building.
buildings=ruins is also suitable, however, using it we lose the former purpose of the building.
That is true. Do note that instead of adding tags like abandoned=yes, it would be better to use lifecycle prefix, (e.g. mark it as abandoned:building=house or whatever).
In EveryDoor for building, as far as I know, you can do that only in manual tag editor (icon in the upper-right part of titlebar which says current building type); there are currently no buttons to set that more easily.
But abandoned:building key is deprecated https://wiki.openstreetmap.org/wiki/Key:abandoned:building
But abandoned:building key is deprecated https://wiki.openstreetmap.org/wiki/Key:abandoned:building
Interesting. Somebody seems to have changed wiki definition last year based only on short comment by one other user on talk page, without any larger discussion. Previous revision looked like this and defined abandoned:building as "A building which has been abandoned and is no longer functional due to serious damage to roof or walls, but which is still visible in the landscape".
They seem to have changed abandoned:building=* to building=ruins (and thus incurred loss of data precision, as you note!) with reasoning that they did it because "it is still a building, even when it doesn't have a roof."
That however disagrees with common wikipedia definition of the building as "enclosed structure with a roof and walls standing more or less permanently in one place" (emphasis mine). So, in my opinion, such change was wrong (and contrary to common mapping practice, especially as building=ruins has its own set of issues/confusion.
Thanks for bringing it to my attention though, I'll comment further on those wiki pages and attempt to rectify the situation. I do agree with adding disused=yes to building=house which is just disused (because it is, as the claim goes, "still a building").
There are also other lifecycle prefixes you might be interested in, which do not seem contested at this time, like ruins:building=*, destroyed:building=*, etc., so you might want to consider them too.
Kinda same as #691. In 5.1 there's a button for setting a lifecycle prefix "demolished", and you could have chosen "ruins" for a building type all along.