>The EU isn't really a country, it's a free trade agreement with an unusually democratic (by the standard of FTAs) process for updating its own rules.

The EU isn't just a free trade agreement and it has never been just a free trade agreement. It has always been a political endeavour.

Of course that doesn't make it a country or a nation state at all, but let's not go too far in the other direction when trying to describe it.

Every free trade agreement is a political endeavour. The entire concept of free trade is in part where the term "liberal" originates from (not that the term should be considered a guide to current policies of parties with that title, lots has changed since it was Liberals vs Whigs).

The EU isn't a country (yet), but it's a political union that increasingly walks and quacks like a country.

https://www.youtube.com/watch?v=_lj127TKu4Q

Indeed it is not a country. But democratic process is a very wrong word here, even with the adjective "representative". The EU process for updating its own rules is a bureaucracy directed by prime ministers, and those influenced/controlled by powerful groups. E.g. Scholz and Macron pushing for federalization and weakening the power of states - this is great for EU apparatus and those wanting to make it stronger, but state citizens do not want this.

Can you name any trade agreement with a more democratic process?

I wouldn't connect those concepts at all. Democratic process is expected in a state that proclaims to be a democracy. Not in a trade agreement of multiple states. Also, EU is not just a trade agreement.