I'm running sodium with the Continuity mod. I heard to download the mod "Indium" for use of the Fabric Rendering API, cause maybe that would be the case, but that mod became out of date since Sodium, apparently, natively supports the Fabric Rendering API. The connecting textures work without the Bare Bones resource pack, but not with it on. Any thoughts?

Are you sure Bare Bones has connected textures for those blocks?

Based on the fact that this addon exists, I will assume that Bare Bones does not have connected textures for glass and bookshelves, meaning this is not a bug.

How do I check cause I just put the pack in and called a day. Is there some configuring I need to do?

No. Not all packs include connected textures. The only way to make for sure is to look at the pack files.