C F G C E Am Dm G
There is no Emaj in C major, but it feels good to put it in.

What is this called in English music terms?tonicisation？ or outside？

Does BIAB have an automatic function to help us choose more chords? Like a suggestion.

Emajor with its G# is a passing tone or "outside" note.

No

Emaj sounds good in there. I like the feeling

I just strummed those chords on my uke and it sounded dandy, the E Major in particular. I wonder if Mr. Mix is aware that he could create a complete song in BIAB using just that progression?

PS — Autocorrect wants me to say that I “streamed“ those chords on my uke.

That is all that matters.

The E-Am-Dm-G is part of the circle of fifths:

https://www.circleoffifths.com/

The E leads to A, A to D, D to G, and the G to C. Note that any of these chords could be major or minor and with or without extensions, i.e. 7th, 9ths, etc.

Note that any chord can come after any chord. The trick is to work back to the tonic key, usually using the circle of fifths. One rarely stays solely in the tonic key. They are called key areas.

I find it quite interesting that you found and like that progression.

The first part is I IV V I, which is very conventional and is part of that common popular set of progressions using I IV V vi that I mentioned elsewhere (the Am is the vi).

The second half starts on a III, which is slightly unusual, but not very unusual (You will often see a III7 used), and the progression from it is III vi ii V and back to I. That III vi ii V I (or 3 6m 2m 5 1 if you prefer) is a stacked pair of ii V (or 2 5) movements around the circle of fifths, resolving to the I. That is the "moving key centres" that I also mentioned.

You might try a slight change and see if it also sounds nice to you.

C F G C E7 Am Dm G7 and back to the C.

Both sound great. That E in its various suggested forms is a really nice surprise.

Some songwriters intentionally transition to a Major-third to give brightness and interest to their compositions, especially for a bridge. That is exactly what you have realized within your chord progression.

The notes of the Major-third are similar to a Augmentation of the root key (C-Aug).

E chord in the key of C is second nature to most guitarists. We all learn Freight Train as one of our first finger picking party pieces and the C-E-F chord sequence is unmistakable.