Inline code is hard to see

Not easily. You could try to target it with CSS attribute selectors… maybe.

A code block will look like this:

<p>
    <code>some code</code>
</p>

and inline code looks like this:

<p>
    "Lorem ipsum "
    <code>some code</code>
     " dolor sit amet."
</p>

The difference is in the quote marks.

But, wouldn’t you want to be consistent and have both with the same background?