UC (new claim): Work-Coaches, Pre-WCA Claimant Commitment, and DEA

I'm very confused by this whole thing. Apologies for the story but I'll need to explain where I've got to.

I made a new claim on health grounds, did the ID bit as one job centre visit and then saw a 'Work Coach' (WC) as a separate appointment (at their behest); this last one was on 3rd Feb.
The WC seemed to be starting from a position of expecting me to be fully capable like a jobseeker, only 'switching off work search requirements' because the mental-health (MH) worker that was with me pushed back on MH grounds (several times). The WC said they were still imposing some directions to 'know what was available' but that the 'work search requirement was switched off'. We therefore understood (quite reasonably I think) that the weird direction didn't really matter too much because it was voluntary. This is the only bit they showed me written down, they said they couldn't give a printout to sign and that I had to go home, sign into the magic portal and agree the claimant 'commitment' there. They also arranged a WFI for 10th March but said not to worry about it and I wouldn't be put under pressure.

When I went to confirm the agreement I found the WC had also put that I need to do their (incoherent) search for 35 hours a week(!). I replied that this hadn't been discussed. They claimed it had, re-stated about having 'switched off work search requirements' (which seems to be rendered meaningless by the content of the agreement) but put it down to 10 hours. I said I can't work-search for that (arbitrary number) either, we haven't discussed work or my capabilities at all and given you have a sick note that makes no 'fitness' exemptions it makes no sense to give me work tasks before the health assessment so please consider me exempt until then.
They claimed 'it doesn't work like that and you have to sign the commitment'. I said please would you seek internal guidance on your procedures for exemption. A Disability Employment Adviser then wrote to say that they would 'explain the claimant journey' and made an appointment but for after the agreement signing deadline. Trying to keep things civil, I said ok fine we'll talk then, but as I still had the agreement unchanged and timing out I settled for stating I would mark it as agreed but was doing this under duress and that I wanted it reviewing at the first opportunity.
The DEA appointment was to be last week but was cancelled (their end). They've since re-scheduled but for after the WFI (13th March).

I would be extremely grateful if someone could explain, or point me to other threads that might explain, what the hell is going on. Are they outright avoiding consideration of substantial risk rules (I have an energy-limiting chronic illness)? Should I ask for the WFI to be postponed until after the DEA? What is the DEA's game? Maybe I'm missing something - I've been over reams of guidance trying to comprehend all the rules and regs until I'm dizzy but still I'm unable work out where I stand. I still haven't got a UC50, btw.
Also note although my G.P. signed the sicknote it's clear I can't count on them for any support or insight into the condition - not entirely unreasonably as it's a specialist medical area they've had no training on (I also don't think they're particularly interested in learning but let's not get into that). Also also, if I'm involving the MH worker note they come with a civilian perspective not a rights-based one.

Much much appreciated if anyone can help.

Thank-you, Chris - I wasn't expecting an approval before tomorrow afternoon I'll work out how to get e-mail notifications for next time!
Yes I'd be interested to hear if this predicament seems familiar to anyone, if I ought to concentrate any complaint on some key issues and leave others aside, whether it's something I can sensibly take on without advocacy, and any experience other members might have in complaints about similar experiences.
NB For my part, I'm currently trying to establish for myself what a DEA is in relation to UC, why they might have been farmed out this task instead of the WC taking responsibility and how still meeting with a WC first is supposed to work (if indeed that is what's supposed to happen!).
Continued thanks in advance to folks for any insight offered.

Update on the role of Disability Employment Advisers, for anyone following.
This gives three internal documents outlining the DEA theory.
After scanning these over, I could cautiously summarise that DEAs work both as an internal adviser to WC on request, and as support to claimant otherwise (presumably not unlike a welfare-to-work leech provider). From this I'm unable to see any compelling reason that a WC should remain involved (I daresay there'll be some half-witted theory behind it. ).
I've also seen a little critique for outside perspectives (Work and Pensions Committee, Chronic Illness Inclusion Project and a coalition of mental health orgs); from those I'm reading that - very broadly - DEAs seem to be welcomed as some injection of sanity, but would be better if WCs weren't also there complicating matters and possibly better still if replaced themselves by VCSE sector support options.