Yes - battery is screwed. And MG won’t accept it!
I can fully understand your frustration regarding to the issues you think have / have not, with your battery pack.
But it’s become a bit of a “Mexican Stand Off” now because the dealer states the pack is fine and you are not convinced at all.
You are 100% convinced that you have had a faulty pack, from day one almost.
And maybe you have ?

.
But if you really really want to contest their findings, you need more concrete / structured evidence to challenge the dealers findings.
You could either find another MG dealer who would provide you with a simple, detailed SOH report on the whole pack.
It is likely to cost you 1 - 2 hours labour ( wait ) but it will hopefully give you something, or nothing that will proof / disprove your deep concerns.
You could take it to an independent EV specialist who could do the same thing, but MG may try to contest these findings ??.
Unfortunately, being brutally honest here.
MG are not about to replace that whole pack, worth about 8 - 10 grand, just because you “think” it is faulty.
I know that sounds really harsh, but that’s the truth.
You absolutely need some hard evidence to get them to look at this case again.
Even a simple OBD dongle is a simple starting point, if this give the slightest incline that something is not 100% then you have made the first steps to progress your claim.
Oh …… Sorry, did you say the BMS module has already been replaced on this car ?.
Am I right in thinking the BMS module lives INSIDE of the battery case ?.
As it does in most EV’s.
If so, if it has been replaced, what gave them due course to replace it in the first place and therefore, did this necessitate removing the pack to install it ?.
I ask, only because this is a huge job and needs special Techs to carry out this level of EV work.
It’s not something your local dealer would take on to be honest.
As this car on a lease deal, I expect that you consider expediting this is not really worth the bother and I get that entirely !.
In fairness though, I don’t think any EV manufacture is going to replace a whole battery pack without some serious evidence to support this type of work / expense.