There are now two pull requests proposing changes to quote toots inside private mentions (DM).
When composing a DM, pasting a link will not create a quote: https://github.com/mastodon/mastodon/pull/36690 When composing a DM, it'll not be sent if it quotes a toot from someone not mentioned: https://github.com/mastodon/mastodon/pull/36689
If approved, the changes will be merged into Mastodon's source code.