I think the deal is not really Brahms but the way that musicology itself kind of came into existence in quite a different way than it had been before the 20th century. Schoenberg is one of the figures, along with Hugo Riemann and later Erwin Ratz, to name a few, who kind of began analyzing music in such a way as to find the things that Brahms did actually special. As a side (but relevant) note, Ratz's book "Einführung in die musikalische Formenlehre. Über Formprinzipien in den Inventionen J.S. Bachs und ihre Bedeutung für die Kompositionstechnik Beethovens", as the name implies in German, is one of the first serious attempts to connect the relevance of Bach's formal experiments with what Beethoven later did in his Sonatas and his concept of "motivisch-thematische Arbeit," which is what Guido Adler called the process which motives and themes are developed during the 'development' segment of the Sonata form. In essence, it means division and sequencing of motives derived from an overall larger theme.
Now why the hell do I say all this? Because this intricate look at how form is put together through these elements brings attention to what Brahms was doing, such as obfuscating the reprise segments of his forms among many other things. There's much to analyze from Brahms which, if looked at with the right analytical lenses, gives you a rather interesting look at how he subverted many of the tropes that were present in Beethoven's standard Sonata model (which he himself also subverts, of course, but that's another thing.) How about a concrete example?
Sonata in F# minor, Op2, first movement. The reprise arguably starts in the FF Furioso mark (my score doesn't have measure numbers, but it's often at the end of page 7) where the theme actually appears but with a variation. Now, normally, if this was Beethoven, this would be a Scheinreprise (false reprise,) since it's not 1:1 what the theme is like at the very start. But if you look later, that is actually the only reprise that follows the rhythm. Later (A Tempo Sempre FF) there is a sequence built on it which has the same model of the original, but by that point it couldn't really be called a reprise either. It's stuff like this that makes Brahms interesting to look at, in my opinion.