Challenges get old and inactive, it happens to all of them. The Showcase is a unique type of challenge, that has done surprisingly well, given the controversies it's faced.
But now, it's pretty much dead AFAIK. New languages keep coming in, but they usually get only 3 or 4 upvotes, which indicates not many people are actually viewing it
As long as new answers are coming in, a challenge isn't dead. Those answers may not get many upvotes, but that shouldn't matter. If you want to showcase your language, do so, regardless of the score - especially now that the limit on snippet lengths has been removed.
Furthermore, for a challenge that is over 5 years old, for new answers to still be getting 3 or 4 upvotes is pretty impressive. Not everyone upvotes every answer they see. I personally will browse a challenge and can give out no upvotes, or upvotes on most answers; in short, you cannot tell how active a challenge is by answer votes.
Good, hard-worked answers are buried in rubbish short answers like the BCT one
First of all, if you don't like an answer, downvote and move on. Second of all, if you think an answer is good and has been worked on hard, upvote it. That's all. The Showcase is constantly active, given that people are always adding new snippets to their answers, so any low-effort answers will get buried and forgotten about soon enough, while constantly maintained answers will always be fairly easily found.
It is no longer working. Closing it is of course a solution, but aren't there positive choices?
Agree to disagree as to "it is no longer working". It constantly gets new answers and updates, so it seems to be working to me. You may not find new languages to learn there (I assume that's what you mean by "no longer working") but others will.
Closing it is absolutely not a solution. Take a look at the accepted answer to the linked discussion. Four years ago, we agreed that closing it wasn't a good solution. We can have a second poll to see how people are feeling, but, given the Showcase's constant activity, I doubt there's much support for closing it.
I also want to mention the problem about the removal of the one-vote-at-a-time rule.
Again, as the accepted answer the last time we had this discussion states, the Showcase is not like most challenges here. The unique showcase tag, along with being a community wiki, and the notice at the top of the challenge body all state "This is not a normal challenge", and therefore, we cannot treat it like a normal challenge. This site may not be the best place for such a thread, but we have it, it's active and popular, and it currently isn't doing any harm.
Several users (myself included) preferred to follow the old rules despite the current community consensus
Well then, you can self-impose the old rules upon your answers. But that isn't a reason to change anything about the challenge. When it was a popularity-contest, there were issues raised about how some newer answers weren't getting enough upvotes to properly compete with older answers. If you wish to constrain yourself by the old rules, then you also have to accept the possible failings of those rules.
And new answers will look different. Yes they do. For example, the recent Integral answer have a 1 byte answer, then 12 bytes, then suddenly 37 bytes.
This is perfectly within the rules of the challenge. You may not like it, and it may be confusing, but it's a perfectly valid answer. Furthermore, as the answers are community wiki, you are always welcome to edit in additional snippets to improve the answer.
This is just boring
That is completely subjective, and what voting is for. If you think an answer (or challenge) is boring, I invite you to leave a downvote and (preferably) a comment explaining why you think the answer/challenge is boring. After that, as long as the answer/challenge is valid/on-topic/acceptable for the site, move on.
Overall, the Showcase isn't a perfect system. But it works as an effective way to demonstrate your language and its interesting features. You personally may not like particular answers, or even the challenge as a whole, but, again, that's what voting's for.
If you think that users aren't fully showcasing their languages, I encourage you to leave an upvote and a comment to show that you're interested in the language and you'd like them to continue showcasing it. Or, if you know of an interesting feature that hasn't been demonstrated, you can always edit it in yourself. Finally, if you think an answer is low-effort, or isn't a good example of the language, you can downvote, or post your own showcase of that language.