From the documentation page on interface layouts that if the script or shader editor windows are split to their own floating panels, this is not persisted between invocations of the editor.
Question is whether this is on the roadmap to be addressed or not, and what sort of timeline we might be looking at for this QoL improvement?
The documentation is out of date. Both of those windows stay popped out and in the location (and screen and size) you left them when you closed the editor. This functionality was added in 4.5.
Awesome. That’ll teach me to go try this stuff out before trusting the docs 
The docs are pretty reliable, but they rely on the community to keep them updated. So, you can at the least add a comment on the current version of the doc about your findings. Or, you can make a document commit and update it yourself.
Good point. Might go make a PR this weekend to correct it.