The look you are going for is not an option with the wood floor as is. Uneven edges with chipped areas. Your only current option is to place a transition that overlaps the wood flooring.

To achieve the look you want first cut back the wood evenly and install a perpendicular piece of wood stopping short of the tile to allow for the profile edge you would like to see.

The metal edging you have pictured typically has an L that is placed underneath the tile to hold it in place. It will not be an option for you after the tile has been installed. Creative Tile is correct. Your best solution is to use a wood transition. Good luck!

Can you have a wider wood piece installed horizontal between the two? You would need to have the old floor cut back to accept the new piece and if using a think enough piece I would think it could be sloped to make the transition less extreme. We had a five inch board used between our brick mud room floor and white oak kitchen floors. We also did a similar install with a marble threshold between the master closet wood floor and the master bath marble floors

Agree w ctec.

Important to note most metal flashings are deco, some are actual expansion strips. You need to use either an expansion strip or allow for an silicone expansion joint at change of materials.