Really odd experience, any (and what) red flags here?

I applied for a QA Manager job at a small high tech manufacturing company last Thursday for a job advertised on LinkedIn that properly linked out to the company's career/hiring page. Got a screening e

I applied for a QA Manager job at a small high tech manufacturing company last Thursday for a job advertised on LinkedIn that properly linked out to the company's career/hiring page. Got a screening email on Friday - including salary expectations which I responded "given the posted range ($xxx-xxx), I would be looking for compensation at the top of the range," submitted my response on Sunday, got an invite for an interview before noon on Monday for an interview on Thursday. Exec Admin, the person I to be replaced, the COO who the position reports to. Showed up at the 1pm interview, was fine. I check all of their boxes (and more) and everyone seemed fine with my responses even to the hard-no behavioural/red-flag barrier questions. I even elicited a couple of room-wide laughs/good feelings from my couple of attempts at levity and the overall vibe was ok. Very far from a dream job but acceptable. Takes me out of my background (life sciences), mostly though. The posted pay range (at the highest end) isn't insulting. Some potential for the job being interesting, sometimes. But no realistic growth opportunities and maybe closes doors to coming back to life sciences. I've been unemployed for coming on 14 months and I need something. I am approaching desperation/actually desperate (and just lying to myself), but worked hard to hide that and I'm certain I didn't have that scent. No way in Hell I was going to let on that I was accepted into the Food Bank program and have been receiving their charity and their subsidized low-cost "dignity" focused grocery affiliates. At 4pm, a couple of hours after the interview, the interview admin (and exec admin to the owner) called me on her personal phone (caller ID started with a male name - her husbands(?), but the surname was correct) asking if I would be open to "shadowing" [the person who I would be replacing] for the week [blahblahblah], starting Monday, before they leave the company on the 30th." The exchange was (under the table...) for $1k (this is about half price) - payable at the end of the week - for 5 days of 8:30-5 starting this Monday, whereupon they would decide whether to make me an offer on paper. I feel that this is pretty unfair to me, but I understand their position to make this offer from a risk management perspective on their behalf. Other than 40+ hours of lost opportunity cost of (mostly fruitlessly) applying for jobs during daylight hours, what downsides/ threat-exposures would this present? The plus side is I get to see if the operation is a total shitshow and dump them if necessary.