If the definition is so open-ended that just that specific part can be have almost diametrally opposite effects depending on how it's interpreted, then it's meaningless and we can only determine what Liberalism really is by looking at the praxis of what it actually does when those who claim to practice it are in power.

The practice of Liberalism is invariably a system were in the more visible and direct ways (mainly the way Justice is enforced) people are given more Liberty than in other systems, yet at the same time that effect is entirelly offset by the second order effects of the resource allocation practices supported by Liberalism and the de facto implementation of the "right to private property" part, since the capture by a few of limited resources systematically restricts the Liberty of most people and the passing of such property from ancestors to descendants keeps such capture (which generally reflects either first-mover advantages or the multiplicative effect of previously held wealth) locked for generations, potentially forever.

I think the plight of Afro-Americans in the US is a wonderful example of how Liberalism in practice works: on one hand Liberals loudly demand equal rights and treatment under the Law for Afro-Americans (this is the visible, positive side), yet at the same time they support and reinforce the very resource allocation systems and interpretation of "right to private property" which keep the poor and downtrodden and their descendants poor and downtrodden, something which in practice seriously affects those who were previously discriminated against, which in America are overwhelmingly Afro-Americans since their ancestors were almost all Slaves: as they were discriminated against including in their access to property, their ancestors did not capture anywhere as many limited resources as the ancestors of those who were not discriminated against, and because how that "right to private property" that the Liberals enforce works, that means that their descendants today are far more likely to be poor, and because of the very system of resource allocation supported by Liberals, poverty means not getting to eat as good food, have access as good healthcare, live in as good housing, sleep in as good beds.

Mistreatment at the hands of the authorities will severely hurt and harm some Afro-Americans at some point of their lives, maybe even for years. Poverty because of "respecting the private property" of those who themselves or their ancestors captured limited resources harms most Afro-Americans 24/7 their whole lives (unsurprisingly, people in poorer areas even have a life expectancy of at least 10 years less than people in richer areas) - overtly Liberals demand "equality" of treatment whilst in practice they support the very systems than locks in the inequality from past discrimination and transform said inequality into life-long suffering.

(To add insult to injury, poverty itself also increases one's likelihood of being mistreated at the hands of the authorities and increases the hurt and harm caused by it)

Liberals claim to want equal treatment for Afro-Americans whilst making sure the very system around them, because of their ancestors having been severely discriminated against, de facto treats them far, far, worse than most others whilst that specific manifestation of injustice (suffering merely because one was born to poor parents) is put forward as "the way things are".

No, it really isn't "the way things are", it's the product of how "right to private property" is interpreted.