Block editor: can’t change format of inline code blocks

Yes, this was a CSS issue.

See this answer on the WordPress forums for a complete answer.

There are two interlocking problems. First, the code style is defined with a more specific selector. Second, the “Additional CSS” is effectively added to the stylesheet at the top, and so the theme’s definition takes precedence. The solution is to use the right selector, and to add !important to the style so that it takes precedence:

*:not(.wp-block-code) > code {
    background-color: #EAF7FF !important;
    color: #0066cc !important;
}