Swing's HTML renderer is old. It supports HTML 3.2 and CSS 1.0, and it does not even support all capabilities of those specifications.
Looking at the documentation of the CSS class, we see that it lists all of the CSS properties it supports. There is a list of what is supported, following by a list prefaced with "The following are modeled, but currently are not rendered." In that list is the float property.
So, Swing HTML rendering does not currently support the float property. At all.
There is a long-standing open bug, Java Bug ID 4296022, for this issue.