Sorry I meant to say Archiving is now natively supported in Linkding!
But I get your point on local copies. Coincidentally I also have a similar setup but entirely on Shortcuts. My point of entry for all my links is Goodlinks. It does exactly what you want in terms of full text archiving (plus has a great reading focused UI). I use a shortcuts automation to check for new links / tag updates on my Goodlinks and send it to my linkding (for wayback style archival).
So funnily enough my problem was exactly diametrically opposite to yours in that I already had full text search with Goodlinks but I didn’t have a true wayback style archival system and I ended up setting linkdng for that
Anyway, I highly recommend you check out Goodlinks though. It has top class UI + robust shortcut integrations