Old to new molding transition
If you're happy with the height of the kitchen baseboard being a little lower, then you could cut a strip off the bottom of the kitchen baseboard so when it rests on the tile, its height matches the lounge baseboard.

You can then mitre the right end to make a neat finish with the lounge. If the baseboard ends here then the left end can be mitred as shown here https://youtu.be/dX2tVUg9r8I or https://youtu.be/8UlntpiHB8k