So, I understand the first sentence, but I'm a little confused about the second one.
My translation is: to have a feeling about a certain matter to the extent of being able to declare about it.
Isn't this an excerpt of a dictionary definition, like what this blog cites?
In this case, it means:
what one thinks/feels about a certain matter (which has taken shape enough to be expressed/presented/published)
As you have correctly translated, 程度 means "(to) the extent/degree", or you could take Vできる程度 altogether as "enough to V". Anyway, both ～程度 and ～程度に stands for the adverbial phrase "to the degree", but the form with に is preferred when describing the state how the result is, while without に the manner how the action is done.
30cm程度切る cut (off) 30cm
30cm程度に切る cut into 30cm pieces or trim into 30cm long
My understanding is that both parts of your sentence describe the
もの mentioned at the very end of the sentence.
A thing that collects the things felt about a certain matter.
A thing that collects (something) to the degree of being able to present (it).
The simple answer: the に in 発表できる程度にまとまったもの allows the adverb of degree 程度(extent) to modify まとまった.
発表できる程度 translates to "the extent it can be presented".
まとまる in this context translates to "to come together; to cohere".
In order to say that ある事柄について感じた事 has まとまった to 発表できる程度, we use に.
becomes, in English:
(The substance of) what you felt about a certain matter (that has become coherent enough to be able to be presented (outwardly)).