std::format of user-defined types?

std::format doesn't support operator<<, you need to provide a formatter specialization for your type (Point) instead. The easiest way to do it is by reusing one of existing formatters, e.g. std::formatter<std::string>:

template <>
struct std::formatter<Point> : std::formatter<std::string> {
  auto format(Point p, format_context& ctx) {
    return formatter<string>::format(
      std::format("[{}, {}]", p.x, p.y), ctx);

This will give you all format specifications supported by std::string out of the box. Here is an example of formatting Point with center alignment padded with '~' to 10 characters:

auto s = std::format("{:~^10}", Point{1, 2});
// s == "~~[1, 2]~~"

which is nontrivial to achieve with iostreams.

You have to specialize std::formatter for your type.

namespace std
    template<class CharT>
    struct formatter<Point, CharT>
        template <typename FormatParseContext>
        auto parse(FormatParseContext& pc)
            // parse formatter args like padding, precision if you support it
            return pc.end(); // returns the iterator to the last parsed character in the format string, in this case we just swallow everything

        template<typename FormatContext>
        auto format(Point p, FormatContext& fc) 
            return std::format_to(fc.out(), "[{}, {}]", p.x, p.y);

I don't think the ostream operator will work but I have no sources to support this claim.