The tailstock is MT2 and MT2 centers fit perfectly. I do have that MT4 ER25 collet holder and I'm wondering how hard it would be to turn it down to fit. I've been using a watchmakers lathe for years and they use 8mm (sometimes 10) collets and I have to say I really like collets. On a watchmaker lathe they are very precise (they have to be to turn 0.1mm wheel pivots and even smaller).
I suspect the use of an "adaptor" as reference is preventing sight of the full picture, here.
A full length MT 3 dead centre (and you do NOT need a "live" one for the HS) should sit much further out at its tip. That is generally further out than a # 2 MT in a #2 to # 3 adapter, too.
You need not invest in a high-grade Riten or Stark center to confirm or no. A few bucks to one of the bargain tool suppliers gets you a serviceable-enough MT 3 Dead Center at low risk of waste.
For the ER on MT4? Don't waste your time trying to turn that tail on a Logan. Get one that just fits. That's a preservation of accuracy issue as much as hardness.
It has to be the "Mothership" after all, for collets normally spec'd as delivering
average TIR to rather good numbers over their large collapse range.
PS: That wide collet range is attractive on the ER system. I don't have the for my kitche sink, yet, but ER-40 and ER-20 for just about everything else.
As... a "last resort" that needs but two sets of collets for the entire shop.
Don't confuse those with conventional "spring" collets though. Made originally for TOOL holding, rather than WORK holding, they can be relatively slow to cycle.
An ER wants scrupulous cleaning, then a fair-decent match to its specified torquing.
If you have a hundred widgets to turn, you'll soon prefer a "C" family collet that fits your lathe over the annoyance of the ER.