Where to get soft touch feel keyboards like 1990s HP XT PCs?

I am not familiar with that specific keyboard, but rubber dome keyboards were common in that period (and remain so!).

I generally don't like them compared to mechanical keyboards, as they have a bit of a "mushy" feel, and you have to push the keys far enough down so that the contact points actually impact the surface, unlike mechanical keyboards, where normally one doesn't need to bottom out the key. They are notable for being very inexpensive to manufacture. They are pretty quiet.

Generally, keyboards with rubber domes aren't explicitly sold as "rubber dome keyboards", as it's seen as a not-premium mechanism. If a keyboard doesn't say anything about its mechanism it's probably rubber dome. Just avoid getting something billed as "mechanical" and you're probably good.

I don't know what you mean by "smoothly". Rubber domes have a non-linear resistance -- that is, there's a certain point where the resistance sharply falls off. There's no "click" at that point, though.

If what you want is no falloff in resistance or auditory or tactile feedback at the point where the key registers, there are some keyswitches designed to do that. They're normally not considered ideal for typing -- where one wants the tactile and some level of auditory feedback -- and are typically marketed to gamers. I believe that Cherry MX Red keyswitches do this, Cherry being a particularly popular mechanical keyswitch manufacturer.

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Apparently they specifically make a silent variant, the Cherry MX Silent Red. You'd probably want to look for a keyboard that uses these, not the switches alone.

Some mechanical keyboard users will also add rubber O-rings to the bottom of the key to further damp sound.

There are some other mechanical keyswitch vendors, and I'd bet that others make analogous keyswitches.