So I tried setting up a test phpMyAdmin instance to reproduce the error, and I see the same error, but after spending a bit of time debugging, I feel I have to recommend what @dls mentioned to you in our Slack, which is that if you use an ssh tunnel, “You can use a local client like MySQL Workbench or HeidiSQL to access the database directly.”
To translate from the blog I linked above to your case, the “bastion” host would be login.ibiblio, and the “rds” host would be mysql.ibiblio.
I’m recommending this approach for two reasons. The first is that we do best-effort to support public webapps, but phpMyAdmin can never be for public consumption. It has to be restricted. Second is that even when restricted, phpMyAdmin has a pretty terrible track record in terms of security, and ibiblio in particular has seen instances of phpMyAdmin getting abused.
In closing, if you’re particularly attached to phpMyAdmin, it may even be possible to combine the ssh tunnel method and phpMyAdmin installed locally to you, but I would start with the simplest possible setup first.