That is the case, that old and legacy style DMs will leak who is DMing who and the times that they're messaging. This has been fixed for well over a year with most client apps supporting a new more private standard for DMs. If your client app is leaking your DM metadata, you could consider using an app that doesn't if you're concerned about it.

That said, we have no DM standard, so it's hard to get clients to support one of the many ways to fix this.