“Liberty” has always meant the freedom of the few to do what they will at the expense of the many.

Absolutely not.

1: the quality or state of being free:

a: the power to do as one pleases

b: freedom from physical restraint

c: freedom from arbitrary or despotic (see despot sense 1) control

d: the positive enjoyment of various social, political, or economic rights and privileges

e: the power of choice

At no point is there a scope of "of the few" nor a qualifier of "at the expense of the many".

“Freedom” is the more general term. Just so you know what you’re getting into when you see that word.

Sure, but not in any way that matters here:

How is the word liberty different from other nouns like it?

The words freedom and license are common synonyms of liberty. While all three words mean "the power or condition of acting without compulsion," liberty suggests release from former restraint or compulsion.

the released prisoner had difficulty adjusting to his new liberty

When could freedom be used to replace liberty?

In some situations, the words freedom and liberty are roughly equivalent. However, freedom has a broad range of application from total absence of restraint to merely a sense of not being unduly hampered or frustrated.

freedom of the press

I'm not sure what issue you take with the word "liberty", but it seems to be chock full of some sort of baggage.

It would be fair to say this group is co-opting the phrase for cheap optics gains and using as something between misdirection and blatant falsehood, given their goals are more akin to "allowed to teach indoctrination of fiction/faith/belief over objective material such as math, science, physics and historical material", but... that's the nature of politics overall. It underscores the importance of critical thinking.