The function of 만 in 바라만보다 and difference from 바라보다

바라만 보다 is not a conjugation of 바라다보다; I do not think that you have read carefully the sources you found.

1. In 바라만 보다 (You should place a space right after 만), 만 is a postpositional particle that indicates an emphasis. The compound verb 바라보다 can be separated into 바라- and 보다 when 만 comes to emphasize it. I have said can because you may also use 바라보기만 하다. 바라다보다 is just another compound verb made of the same verbs (바라다 and 보다); 바라다 means to glance toward something here (not "to hope, want, etc." here).

2. Archaic means old and no longer used, but those words are still used. They are not poetic either because they themselves do not express emotions in a sensitive or moving way. It is just that you can easily find them in the lyrics of songs. I would say that 바라다 alone is now unlikely to be used to mean to glance toward something because there are other verbs used often, such as 바라보다 and 보다.

3. They are usable in speech. One thing I should say is that people much prefer 바라보다 to 바라다보다.

I think it's best understood as an analogy of a pattern: (main verb)+만+(aux. verb), meaning "only (verb)". Some examples:

아무 말도 없이 걷고만 있다. [He] is only walking without a word.

부끄러워 죽고만 싶다. [I] am so ashmed that I only want to die.

여기 올려만 놓으면 됩니다. You only have to place it up here.

Now, I feel that "바라만 보다" is a bit unusual(?) because it's not exactly two verbs "바라다"+"보다" - its primary meaning ("stare") is different enough from 바라다 ("hope"), so it's best considered a new verb in its own. However, etymologically speaking, it's still a combination of "바라" + "보다", and apparently the structure is still visible enough that one can insert "만" in the middle.

Also, I don't think it's that archaic. I can imagine it being used in everyday speech, like "뭘 그렇게 멍하니 바라만 보냐?"