Brake master cylinder change / booster question

Hi,I had what seems to me like master cylinder seal failure on my early 308. The symptoms were that the brake pedal went to the floor, then in an "emergency pump" there was a little retardation but not much. Quite "exciting" coming up to a braking area on a circuit....
Master cylinder seals were done about 15 years ago, not by me but in my ownership.
Anyhow, I've taken the master cylinder off and bought a replacement, and also removed the reservoir to re-use that.
My question is about the lever that comes out of the brake booster into the master cylinder. It basically just came out too, though not fully as there is a seal. I can put it back in the booster and it seems to locate centrally, but is that normal? I guess it can't go anywhere when the master cylinder is back in place, but just thought I'd check.
I'd add the booster was working fine.
Many thanks!

 

Many thanks

 

Thank you very much for taking the time to post that (and to make the videos), really helpful and I appreciate it.