Congratulations on acquiring such a nice piece tea tray.
As you said, the problem with wood tea tray is the durability upon prolonged use.
The water that absorbed by the wood exerts capillary force to the pore wall from inside. And repetitive drying and wetting will tear the material from inside.
If you live in an area where winter is very dry and summer very humid, you can see the tomobako box sent from Japan will slightly curved after some time because of the same reason.
While not an expert, I do agree with other earlier comments to put oil regularly on the surface. I did this also to our decorative wood carving at home and observed that wood carving from less dense material that is not treated with oil develop crack comparing to the oiled one.
The wood carving vendor suggested some traditional oil made of Aleurites moluccana nut.
Worrying to experience the same thing with tea tray, I specifically only use porcelain or ceramic tea tray like this.