Hi @Samara1,
Staining timber to match a painted surface would be difficult. It's hard to determine what stain would best mimic that look, as the paint is opaque, whereas a stain is semi-translucent.
I'd recommend you take your pictures into your nearest Bunnings store and have a look at the selection of stains on the timber samples. You can then pick up a colour of your choosing and try it on a test section to ensure you are happy with it before committing to the whole door.
You can check out colours onย Cabot's website,ย too. Perhaps something like Mission brown would be similar.
Please let me know if you have any questions.
Mitchell