Something happened, I didn't mean to change this task' s status.

This is normally addressed by the citation bot (https://en.wikipedia.org/wiki/User:Citation_bot), which "links to open access repositories" (bot operated by @Smith609).

However, given the large number of <ref> without open-access URLs (while one exists), it is unclear how often the citation bot goes through the pages.

Citation bot is currently activated by users, who keep an eye on its output; as such it is not yet processing large volumes of pages. The plan is to deploy it at a larger scale in the near future (next couple of months), at which point openURLs will start appearing more widely.

Good to know, thanks @Smith609

at which point openURLs will start appearing more widely.

That will be a major milestone for open-access and open-science.

Is there a way to trigger Citation Bot on a specific page?

Absolutely! See https://en.wikipedia.org/wiki/Wikipedia:UCB for details.

https://tools.wmflabs.org/citations/ works! Thanks!

The conference papers are rewritten as 'cite book'. However, the OA URL points to the article itself
(and not to the whole proceedings).

As a result, the link to paper is on the proceedings name and not in the title.
For instance
"Proceedings of ISSTA, Demonstration Track"
https://hal.archives-ouvertes.fr/hal-01321615/file/astor.pdf points to "ASTOR: A Program Repair
Library for Java"
(on https://en.wikipedia.org/wiki/Automatic_bug_fixing)

This is confusing both for human readers and for search engines.

What would be good solutions to this problem?

I'd suggest popping a note on https://en.wikipedia.org/wiki/User_talk:Citation_bot, where the other maintainers (who have a little more time on their hands) will be able to look into the problem and suggest a solution.

Thanks for the suggestion, done:
https://en.wikipedia.org/wiki/User_talk:Citation_bot#Confusing_links_for_conference_papers

For the record, OABot is also related to this task: https://en.wikipedia.org/wiki/Wikipedia:OABOT

I confirm that citation-bot calls the oadoi API, and adds the corresponding links (see function get_open_access_url() in Template.php).

This means that once it will be massively deployed, we'll have plenty of open-access URLs popping up instead of no url or paywall urls.