As an update I contacted Citizens Advice Bureau Help to Claim a few times briefly.
Once briefly they said that if I missed the managed migration deadline my housing benefit would stop after that. The adviser was not sure if esa would stop.
When I called them back a few days later - I did not understand it all - but I think I understood that my benefits would stop but at different dates? I was told that if we missed the managed migration deadline, if we apply within another month we can still get the transitional protection. I asked if we receive a letter with a new final deadline, I was told they do not necessarily send a letter.
They said despite the fact we can apply within a month after the managed migration deadline, there were various problems, such as the transitional protection not being maintained when it should. Yes benefits will be stopped but it was too difficult for me to understand and I do not want to induce anyone in error. So if someone is in my situation it is better for them to call CAB Help to Claim and double check with them.
Basically what I gathered is that missing the managed migration deadline comes with many problems regarding benefits being stopped, transitional protection not being maintained when it should have been, so I am not going to miss the final deadline.