If it were my blog I'd mostly go with option 1, and only exercise option 2 if there's a good reason for doing so. (I'd be sympathetic to request to change/remove reference to a deadname, and if it was clear that someone's account had been hacked, but the other examples you cite range from impractical (deleted Tweet) to bonkers (copyright).)

And oEmbed, quite apart from the faff required to implement, would have the side-effect of having sundry social network's stuff poking into your website — possibly jarring, definitely a concern if said network is off the snoopy or security-bug-ignoring kind. (Which, unfortunately, means the majority of social networks.)