You conveniently cut out the next definition in your page where it says that it is related to liberalism.

And the leftism ideologies isn't simply being open-minded. It is actively promoting new ideas and policies that benefits the citizens. This is why we use the term progressive.

Liberal is firmly center right on the political compass and even the definition you post ad nauseum is indicative of that.

I've noticed that it's generally a bad idea to discuss ideologies by label. If I talk about soviet communism, am I talking about what Lenin and Stalin practiced in the USSR, or the ideals from which they started and mixed with pragmatic realist policies, eventually allowing corruption to pervade?

Talking about liberalism or leftism as if it is a unified, monolithic ideology only confuses people. Even specific movements (say the Christian nationalist movement in the United States) there is still some ambiguity. They want the US to be a Christian nation, but don't agree on which denominations would be privileged (say, can serve office), are legal among citizens or are criminal.

When I talk about ideological principles and want to be clear, I talk about specifics. e.g. Everyone should be equal under law. Minors should have the same civil rights that adults do. Street drugs should be decriminalized, and drug epidemics should focus on treatment and mitigation. Force should be a last resort by law enforcement, not used just because a civilian has an unknown object in their hand.

No, liberalism means liberal, even outside America.

those pertaining to the liberal ideology (not the liberalism ideology)

This is confusing, you seem to be using colloquial definitions of liberal with political ones interchangeably, but in the context of the political right denouncing liberal political projects as "woke" suggests you mean political liberals in the US.

When I see liberal parties in other countries, namely Europe, they are classed as center-right. Here in Canada they're a little more spread out but economic right for sure. For just a quick example, I support strong affirmative action, but for political liberals that has become watered down to "equality of opportunity" and disparity frameworks.

For someone who's chief complaint is "leftists are really bad at communicating our ideas", you might want to sit back and really think about what you're doing right now.

Liberal ≠ liberalism. I’ve had to explain this so many damn times in this thread it’s beginning to make me nutty.

It's because you're using liberal as in, "wow that was a really liberal amount of gravy," synonymously with liberal as in, "a supporter of a political and social philosophy that promotes individual rights, civil liberties, democracy, and free enterprise."