I can't change the font of H2, H3 headings in my posts.
When you select the block you can see the different heading options on the top.

None of these heading options does anything but resize. Can you not change the actual font (ital, underline, etc) of a heading?
The heading size is generally based on the theme you are using. This is limited by design.
However, you _can_ edit the HTML of the block and add an inline CSS style.
That seems rather inconvenient for an “updated” editor. Especially considering the classic editor allows you to easily customize all of the formatting without any css or html
I agree; I understand the philosophy behind separating headings into their own blocks but it's really not intuitive or easy to actually use. The extra clicking to make new blocks and select headings makes writing even more tedious than intended. It'd be great if the headings could be grouped with the other options by default- whether that means separating the headings into separate blocks once the user selects out of it or if it forms part of the paragraph is up for debate.
Closing this issue as it is now possible to change the font style and size for the heading block:

Font style (bold, italic) can be changed in the block toolbar, and font size can be adjusted in the block settings menu.
Most helpful comment
That seems rather inconvenient for an “updated” editor. Especially considering the classic editor allows you to easily customize all of the formatting without any css or html