How to transfer from one freighter to another?

I have a B-class freighter from early game (bought soon after they got released, 2016 or so), spent a good amount of time investing in it, but most importantly: I have a huge mount of resources.

I would like to swap it for an S-class freighter (RNJesus permitted), but before I commit to the search/grind, I have questions:

• How to move stuff over from one frigate to another? Is there any way to automate at least some portions of it?
• Is it even worth it?
• The wiki says "The first two saved freighters will always be regular freighters with at most 19 inventory slots. Starting with the third freighter, they will always be Capital Freighters." - Does that still hold true? Where do you even switch between the freighters?