Search your feelings

I mean you're probably closer to a true moderate liberal than Joe Biden or other American Democrats that call themselves moderate liberals. You're not left wing, since you still think capitalism can work if you just do enough state power, but Joe Biden would call you a far left communist out to destroy American values same as Trump or Nixon.

Hint: These stuff is not what most other "moderates" would support. You sound like a very confused progressive lib.

In my country, most of the right also support these things adamantly, just not as liberally as the centre or left.

You probably are more traditionally centre. But on the US spectrum, there's some that would consider you more progressive or left. While in other countries, you could be more right—shrug. You need to realise the US Republican party, as far as popular parties go, is considered the most extreme right-wing party in the western world and the Democratic Party is perceived as right of centre. The US spectrum doesn't recognise that because of the big right-shift in the domestic spectrum.

But I wouldn't worry so much. People that invest everything into the 2D spectrum, let alone single points on it, aren't really perceiving your true positions correctly anyway. Hence why you can say a thing and be put all over the place by these comments, depending on individuals' ideas of it.

Don't waste our time, please. Just use the standard American definitions when chatting about domestic American politics. It's not so hard.