I’m really curious does anyone here have more experience or knowledge about encoding data into DNA for things like Bitcoin keys?
I don't think anyone will do that. This kind of technique requires highly sophisticated equipment and specific environment which includes strict biosafety controls, contamination prevention, environmental controls, and more. All of these requirements are far beyond what home user could manage. As for third-party services that might offer this kind of work, I doubt anyone would be willing to hand over their seed phrase to them.