Liberalism has several meanings, it depends on the context whether it’s right or left leaning.

Liberalism has one broad meaning, ie an ideology supportive of individual liberty through strong private property rights and ideals of class mobility. Ie, it’s the underlying ideology tied to Capitalism. This ideology can be to the left or right of locational medians, but in the international context of leftism vs rightism it is firmly right-wing.

Typically, in Europe, the traditional right leaning parties would call themselves “liberal”. Their philosophy is classic liberalism, which places an emphasis on economic freedoms, like a free market, limited government, laissez-faire policies,…

See my previous paragraph, this is the correct form.

When conservatives in the US call people “damn libruls”, they are referring to people with a philosophy of social liberalism, which places an emphasis on social justice, political freedoms, civil rights, individual autonomy, … This is the left leaning version of liberalism.

Not quite. Social liberalism is tied to economic liberalism to form “Liberalism” overall. These ideas are tied together for one cohesive world view. A Marxist or an Anarchist is likely going to be more progressive than Liberalism when it comes to Social Issues. Referring overall to “Liberals” as left-leaning simply for the fact that the social aspect of liberalism is progressive fails to take the intertwined economic aspects into account.

Nothing exists without context, trying to chop ideologies into their component parts without recognizing the context of these components is an error.