Unpublished paper with published followup gathers citations: should it be published?

I see no reason that you really need to do anything with the first paper. In arXiv it is a stable, citable resource, people are finding it useful, and the citations are accruing credit to your work.

If you are concerned that people who are reading the first paper are unaware that it is obsolete, then you can add update its entry to add a pointer to the second paper. People will still likely continue to cite the first paper, however, either because they have reason to prefer it or because it's already in their reference collection and they don't revisit and see your update.

Other than providing a pointer to the second paper, though, I see no reason not to just let well enough alone, be grateful the people are appreciating your work, and move forward onto other things.

Based on your comment

The basic idea behind is very similar. The reason the second one is better is due mostly to improvement of several details, which in the end made the results more trustworthy.

this sounds to me like you could consider the arXiv paper to be an earlier draft of the second paper, in which case you've basically already published it (as the second paper).

Presumably anything novel in the arXiv paper is no longer novel in the field because it is either established directly (or superseded) by the second paper, or the second paper cites your arXiv paper directly.

As @Vladhagen mentions in a comment, if you do decide to continue with an attempt to submit the earlier work, you will need to be clear about the existence of the second paper to any journals you submit it to, and given the similarities you should certainly be citing your second paper in the new submission anyways. If anything, that self-citation would be the purpose of submitting the previous work, in order to direct more attention towards your second paper.