This all just seems a bit strange to me?

When you were claiming ESA you were in the WRAG and you started your claim before April 2017 this means that for ESA you were entitled to the extra WRAG component which was why you were claiming £204 per week. If your claim had started after April 2017 then your fortnightly money would have been £146.20.

When you transferred to UC you should have been given the same award that you had when you claimed ESA which for UC is LCW. This pays an extra £126 per month. Looking at your calculations above your monthly money is missing the LCW element which is £126 month extra. This will be why your online journal is telling you, you need to look for work.

What you need to do is ring ESA and ask for a call back from a case manager. When you get the call back you need to tell them that you transferred to UC and ask them to send across the award you had for ESA to UC. Once this is done you'll be paid the extra money and your work commitments will be changed and you won't be required to look for work.