White Council inconsistency?

[JeyEn]

Hello! So I stumbled upon this topic while reading about Gandalf seeking the truth about Bilbo's ring.

Someone said how could Gandalf forgot about Saruman's words about Great Rings having a gem. Then I started to search what the White Council talked about in their meetings. And I think I ran into some continuity error.

In 2941 they attacked Dol Guldur. In Silmarillion it is said they talked about Rings of Power and that Saruman said The One is lost to the sea. However since the text about Third Age in Silmarillion feels so strange and is probably heavily edited by Christopher, I am not sure how can I take this as a source.

In 2953 they talked again about Rings of Power. In Appendix B, it is said Saruman talked about the One being lost at the sea for the first time.

However in Council of Elrond, Gandalf said Saruman assured them The One is lost repeatedly.

Is is possible there is an error in Appendix B?

Also -- Gandalf said he half-heeded Saruman's word about gems. Which seems strange, since he (probably) knew about Bilbo's ring and was worried about it. Is there some summary about White Council and what exactly they talked about? To create some timeline.

Thanks!