ADP impact of UC claim

Some advice/guidance required please. (My wife receives ADP.)

Back in May, with nearly zero warning, I lost my job after the head of the company suffered significant mental health issues which impacted the business and resulted in it closing. (Officially I was a self employed contractor, doing self assessment for tax, etc). Since then I've been applying for jobs and we've been living off savings, , selling stuff on ebay to make funds stretch, etc.

Despite getting close a bunch of times it got to the end of November and still no offer of employment. I did pick up some ad-hoc work to top things up over the last 3-4 months (and minimise the CV gap) but was getting concerned about the ever dwindling funds running out and hiring likely being slow over Christmas, etc.

So, I applied for Universal Credit and began that process (it was the benefit suggested as my previously self employed status ruled out other benefits).

Fortunately, just the other day, I received a job offer which I accepted and have signed the contract today. (Woo hoo!) It starts in January so my pay will begin at the end of January. Universal Credit is therefore for a single month/month and a half or so to cover any shortfall between now and then.

Anyway, it was explained to us that it is not the individual who claims, it is the household when it comes to Universal Credit. So my wife also added her details to the claim. She is on another benefit, Adult Disability Payment from the Scottish Government which she moved to as part of the nationwide migration of people from DLA (administered by the DWP). Her award was indefinite as she has long term health issues which will not resolve and stop her from working. She has been on this for about 20 years and throughout that, as well as working, I have been her carer.

Now this claim has sent her into two different streams of requirements:

1. She has a call with the Job Centre for a "First Commitments" interview with a work coach.
2. The Job Centre asked that she get a "fit note" from our GP. We contacted the GP and was told "We are unsure if this requires a sick note or a letter so we need to check with our DWP representative to clarify which. You'll have to have an appointment with the DWP representative". She asked for phone appointment and that was agreed.

On point 2, we queried the validity of needing a "fit note" as my wife is unable to work, is not seeking work. She has too many health issues which impact here daily life and so can't work, hence the indefinite award but we were told by the job centre it was needed.

My understanding is that Scottish people, like my wife, who have been moved to the Adult Disability Payment, managed by Social Security Scotland and who have an indefinite award will not require any assessment/re-assessment, unless there is a change in physical circumstances (e.g. health gets worse).

Our concern is mostly with the 2nd part of process, the DWP involvement via the GP.

Is there any risk to her Adult Disability Payment from going through the DWP interview for the fit note? We are confident she is eligible for the Adult Disability Payment given her major health issues but you hear so many cautionary tales of people being removed or assessed incorrectly and we don't want to end up in that scenario where she might lose the ADP benefit or end up in a broken process. Are there any examples of Adult Disability Payment being removed from someone for applying for Universal Credit? Anything we should be wary of? Also, is it usually a requirement in this scenario to provide a fit note even though everyone knows she can't work?

I'd rather drop out of the UC process and struggle through to the first wage, somehow, rather than risk the ADP long term which would significantly impact my wife but maybe there is no risk?