I think you’re going to have to put in a feature request in the OH UI repository. It doesn’t look like the oh-input is currently configured for this. Right now the oh-input identifies any use of a date based input type and then performs specialized formatting of the item state to match that input type. However it bases that identification on whether the string "date" is found at the front of the type parameter. So, a type of time is not detected as a “date” input type and the pre-existing item state is not formatted.
The repository is here:
https://github.com/openhab/openhab-webui
And if you’ve never filed an issue before then you may find this helpful: