Because when you feel threatened, you are fine that your government passes laws (e.g., surveillance laws) you would never let them to pass.

You don't go out of your way to place a base near another state unless you consider them a threat, or consider them no threat at all but want to conquer them in the near future. I think the former is more likely the intention in this case. If a state's not perceived as a threat and also isn't a likely target for a very one-sided invasion, you probably don't care much about having bases near them.

This dynamic is behind military build-ups, arms races, and increasing tensions and effective ability to act threateningly. You believe a state threatens yours, so you build up on their border, now you threaten them, so they build up more, repeat. Notably this does not happen if neither side perceives the other as threatening in the first place.

IOW placing a base on a rival state's border both is threatening and is also exactly what one does when one perceives same rival as a threat.

There are many vectors that foreign adversaries can be a threat. In Russia's case, they are a threat to our Democratic institutions, but more so a threat to our allies in the region. They are a country well known for their desire for expansion into adjacent nations, even after the fall of the USSR. That's the #1 reason neighboring nations are our/NATOs allies, because they are in fear of Russia.

That base was there long before "the western mainstream media [talked] about Russia being a threat". Its original purpose was to support operations Afghanistan.

Look on a map -- the base is nowhere near Russia proper. You'd have to go well north through the rest of Uzbekistan, then Kazakhstan. If anything it is a statement to Pakistan or Iran.