Help with Migration to UC

Hello, I need some help. I receive ESA IR at £363.80 a fortnight and PIP at Enhanced Daily living & Enhanced Mobility. This is quite complicated but I will try to be concise. Apologies in advance for the long post. Any help and advice you can give would be greatly appreciated.

My partner has lived me with since 2017. The DWP knew about this, but because she was an asylum seeker, she had no access to public funds. So I was kept on a single claim. In November 2021 she was granted Discretionary Leave to Remain in the UK until May 2024. She was also given recourse to public funds until May 2024, at which point she will need to apply for an extension (Home Office talk for "pay us £1,033 and we will let you stay").

When she was granted leave to remain, I contacted the DWP and told them that she had been granted leave and was just starting to set herself up as a freelance musician. The DWP then added her to my ESA claim, raising it to £362.80 a fortnight from £276.70. The DWP sent a form for us to fill out, which we did. On the form, we listed her earnings for December 2021, which were two commissions for recording vocals for two songs. One month ago my partner received a letter from the Home Office telling her that there was a mistake and that she had no entitlement to public funds, but could apply for them but with no guarantee of receiving them. I then reported this to to the DWP. The call agent I spoke to found this very confusing and said this would have to passed up to a decision maker, for they would need to decide whether she could have access to benefits or not.

This week, after repeatedly contacting the DWP over the last eight weeks trying to find out how my ESA would be affected by her earnings, they rang me to say that they had calculated her earnings at £281 a week. They took her earnings for December plus the £200 a month she receives for playing the organ at two churches, and extrapolated this to cover the whole year. If I have calculated this right, that means they are reducing my ESA payments to £80 a month. What they don't seem to understand, which I have made clear on the form as well as the cover letter, is that her work is sporadic and not constant, as she is self-employed and her business needs time to even take off!

My local council has advised me to claim UC, as her earnings would be taken into account every month instead of only once a year.

Here are my questions:

1) The DWP have not forced me to move to UC; I expected them to do this but they haven't. Do I need to make a claim for UC myself, or can they move me themselves? I have been on ESA IR for four years and such have been receiving NI contributions paid on my behalf, as such would I be be given new style ESA automatically or would I need to make a new claim? Or would I not be given new ESA at all and would I have to stay on basic UC?

2) It is my understanding that under the new ESA, my benefits would not be affected by her earnings. Is this true?