https://imgur.com/a/NuGb3zD

I play this mod with SE, K2, and LTN. As you see, Vanilla train stuff doesn't add to the transport group. Is it a bug or an intended thing?

Neither bug nor intended, but most probably modified by mods in the later data stages.
Your should know that many overhaul mods love (or have a need) to change vanilla items in their own ways, and not all of them will be aware and support my mods.

So please request to revise the (sub)group settings in those mod(s) that have done such edits. (Can be read from the blue line under the item name, in their item tooltip.) I do not play (at least not spending enough time on) with most of these overhaul mods, so I will not use my judgement here.
Nevertheless, I have no interest in initiating a "war of final edit" to enforce other mods in accepting my idea of dedicated group and subgroups. If they decide that their own group settings will be better for their overhaul experience, I will not be against that.

I think it's SE? I can see 'vanilla > Schall Transport Group > SE' in the item tooltip. I can't fully understand what's going on... Is there any way to change groups manually?

It is the list and order of mods creating and modifying the item, but SE took the final edit.
So you asked about why the items not showing up in my group tab? This line explains it.

To verify, try disabling SE and see if the items are moved to my group tab properly.

Disabling SE, items are moved properly. I think SE makes two separate subgroups to one subgroup. So is there a way to fix this problem?

As mentioned in policy and previous replies, please request SE to revise the subgroup settings and add the support.
Instructions for the code is written on FAQ page.