See this request: Extract to specified heading with Note Composer. Within the thread, there is a link to a very helpful Templater script by @AlanG that accomplishes what you are looking for: Extract to specified heading with Note Composer - #9 by AlanG. The script was originally posted by him on this thread Templater: open file in new tab and append to end of file - #10 by I-d-as.
I nearly marked it as a solution except for the fact that it doesn’t allow you to choose which heading in the target note to extract the block or heading into.
As a side note, If you scroll towards the bottom of the linked thread you will also see a post I made where I slightly altered AlanG’s script so that it creates bidirectional linking. Extract to specified heading with Note Composer - #13 by I-d-as
I could see someone developing a plugin that is like a new and improved Note Composer. It could have all types of additional functionality like these scripts accomplish, in addition to allowing for choice of Template, as discussed here: Extract to specified heading with Note Composer - #16 by I-d-as, then partially addressed here: Extract to specified heading with Note Composer - #17 by AlanG.
It could also update the resulting broken links that occur when an already linked-to heading is extracted, as requested here: Note Composer: links to blocks and headers should be updated when extracting.
Hope this helps! Good luck!