The passages that you describe as "worthless philosophical ramblings" are part of Tarski's results. He could not have left them out without obscuring the meaning of his proofs. Possibly model theory would not exist today had he done so. It would certainly have taken longer to develop.

Another instructive example is Per Martin-Lof's lectures On the Meanings of the Logical Constants and the Justifications of the Logical Laws: https://www.ae-info.org/attach/User/Martin-L%c3%b6f_Per/Othe.... Unlike Tarski's paper, this contains no formal proofs whatsoever; if the sentence you quote is worthless, then I imagine "There is no evidence outside our actual or possible experience of it. The notion of evidence is by its very nature subject related, relative to the knowing subject, that is, in Kantian terminology." is worse than worthless. Nevertheless these lectures have been of great importance in logic and computer science. You can see some of their impact in the citations here: https://scholar.google.com/scholar?cites=2483744927635326348

You may be unable to find any useful meaning in this kind of writing, but most mathematicians do not share your difficulty. This is fortunate, since the field would be greatly impoverished if it purged itself of all philosophy and philosophy-adjacent work. I would normally encourage you to read https://terrytao.wordpress.com/career-advice/theres-more-to-... on the role of non-rigorous big picture thinking in mathematics, but it deals entirely with human understanding of mathematics and is therefore only of interest to Terence Tao and other such pseudoscientists.