The tag natural=peninsula has been in use for a number of years, but early this year was discussed and approved. Previously place=peninsula was also common. But usage of natural=peninsula is now significantly more common:

https://wiki.openstreetmap.org/wiki/Tag:natural=peninsula
https://taginfo.openstreetmap.org/tags/?key=natural&value=peninsula - Used 586 times

To encourage consistent use of natural=peninsula instead of natural=cape or place=locality for these features, it would be beneficial to render the name with a text label.

The majority of natural=peninsula features are mapped as nodes. The style and initial zoom level could be similar to natural=cape, probably starting z14 or z15 for both nodes and areas, though this would require testing.

(natural=cape currently is rendered from z14, and place=locality is now rendered from z16, though previously it had been rendered from z15)