I don't think I'd automate it, especially because going forward that content is something that whoever posted, intended the post to go to reddit, not lemmy. Especially if it's someone asking for advice or something personal like that.
However, if it's a link to a youtube video or a tiktok or a news article or something, I see no reason why you couldn't essentially cross post that. But again, I don't think I'd automate it because then if they added some sort of commentary around it, you'd be just copying them. But copy the link and add your own commentary, I think that's fine.
Oooh, I like this idea... I've thought about running vaultwarden but like you I pay for bitwarden premium because I think it's critical for me and I like the service and want to see them continue. Using it as a backup, then I can still support them and run my own backup.