I can confirm that custom homecities can be made with xml files. I’m modding the Act 1 Campaign currently and part of that is enabling homecity shipments and assigning the player a deck. The game is a bit finicky though, and for some reason using the “Set HC” button in the Player Data menu only works if the xml file I’m switching to is in the same location as the original homecitySPCAct1.xml file. I’m not certain but I’m assuming that this is only an issue for editing Campaign maps.
Incidentally, all Home Cities created are saved in your Savegame folder as xml files, so if you’re not planning on using cards from multiple civs you can design your decks ingame, save them, and then copy them from the respective sp_ or mp_[CIVNAME]_homecity.xml.
As for whether decks are saved with scenarios I’m assuming so but I’ve noticed that whenever I make changes to my homecity file and then playtest, the game rereads the deck and updates it. Maybe this is unique to playtesting though, I have very little experience in the AOE3 editor.
Update: I followed one of your links and saw this post Scenario Editor: Homecity & Deckbuilding of Scenarios not really possible ingame - #8 by SoullessHeathen
Now I understand why it sometimes fails. What I do (to make it work) is I copy an unchanged homecity file with a valid checksum, do Set HC, and then proceed to modify it in VSCode.