Faculty TT verbal offer made, but no written offer (it's been about 10 business days)

A “verbal offer” is not an offer. in the US, any self-respecting institution would at the very least document their desire to extend you an offer in an email sent in very close proximity (same day, or next day) to the “verbal offer”. The actual offer including a precise salary anount and other hiring package information might take a couple of weeks after that, and official, final approval (typically by a university provost or other high-ranking official) might even take a few months, although that part is usually considered a rubber stamp that’s certain enough to happen that people will move across the country and even buy a house before it happens. But do not let anyone mislead you into thinking you have any sort of offer until something is, at the very least, documented in writing.

It is encouraging that someone says they want to hire you. I hope all will end well and that this is nothing more than an example of a mildly incompetent bureaucracy. But yes, they can change their mind (I have seen it happen), and yes, it is a red flag of sorts, or at least a yellow one. I advise you not to assume anything and to proceed with all other interviews as scheduled until your offer is extended in writing, with precise salary information. Good luck!

Edit after reading @DanRomik 's answer. I think he's right. I misread the question, equating "verbal" with "informal" which I misinterpreted as email from someone with authority. Without at least that I'd be concerned.

Academic mills grind slowly, particularly in December. Particularly at state schools. Particularly now in covid times. I don't think there's cause to worry (yet). I think the chance that they will change their mind is negligible.

Soon you will want to tell the other schools you're not coming (or zooming) for an interview. The sooner they know that the happier they will be. You could tell your contact at this school you need to know your status in order to cancel elsewhere.

Congratulations on hearing first about your first choice.

As others have said, an overburdened, COVID-disrupted, and not very competent bureaucracy seems the most likely explanation, and you probably just need to be patient. That being said, there are high profile examples of major snafus in such a situation (google University of Toronto Valentina Azarova for an ongoing one right now) and lower-profile examples of surprise budget cuts and unexpected hiring freezes. So you can't count your chickens before they hatch.

I'd normally suggest giving your contact 48 hours to answer your most recent followup, though due to essentially everything shutting down at end of this week, you might need to accelerate that a bit. Then try to have a phone or Zoom chat with them, not to pressure them (they're doubtless trying!) but to understand the situation. Has the authorized decisionmaker informally said yes, just not signed the letter yet? Has the budget and terms of the offer been syndicated? Be upfront that you're trying to understand how much stock you can place in the verbal offer made. If you clearly make the conversation about "what can you tell me to reassure me" rather than "I'm going to yell at you for not having been successful yet in sorting this out", you'll get a better read of the situation. Ask open ended questions rather than closed, investigative ones, and try to have a chat, not an email exchange. You want to understand the situation, not have your contact fire off yet another email internally and continue to tell you nothing.

Finally, while you do want to let other institutions know you're off the market, and doubtless you and your family want to celebrate and start planning your move over the holidays, you do need to proceed cautiously and not burn any bridges yet. You are very close to having a confirmed position at your first choice institution, but you need to proceed as if that is not yet 100% confirmed. Even though it seems extremely likely it will be.