how can I properly extend the gutenberg terms block?

It seems like you’re not using a build step to process your custom-terms-block.js. This means you cannot use JSX syntax. Instead, you should replace all instances of JSX with React.createElement():

edit: (props) => {
  const { terms } = props.attributes;

  // Fetch terms and their associated ACF brand_logo fields
  const [taxonomyTerms, error] = useEntityProp("taxonomy", "category", "terms");

  if (error) {
    console.error("Error fetching terms:", error);
    return React.createElement("div", {}, "Error: Could not load terms");
  }

  const termsWithLogos = taxonomyTerms.map((term) => {
    const brandLogoUrl = term.meta?.brand_logo || "";
    return {
      id: term.id,
      name: term.name,
      brandLogoUrl,
    };
  });

  return React.createElement(
    "ul",
    {},
    termsWithLogos.map((term) =>
      React.createElement(
        "li",
        { key: term.id },
        term.brandLogoUrl
          ? React.createElement("img", {
              src: term.brandLogoUrl,
              alt: term.name,
            })
          : RichText.Content({ value: term.name }),
      ),
    ),
    termsWithLogos.length === 0 &&
      React.createElement("li", {}, "No terms found"),
  );
};