You're right: the Fregean/neo-Fregean talk of analytic truths is not one-to-one (so to say) with Kant's such talk. The SEP article on the analytic/synthetic distinction notes:
Kant tried to spell out his “containment” metaphor for the analytic in two ways. To see that any of set II is true, he wrote, “I need only to analyze the concept, i.e., become conscious of the manifold that I always think in it, in order to encounter this predicate therein” (B10). But then, picking up a suggestion of Leibniz, he went on to claim:
I merely draw out the predicate in accordance with the principle of contradiction, and can thereby at the same time become conscious of the necessity of the judgment. (B11)
As Jerrold Katz (1988) emphasized, this second definition is significantly different from the “containment” idea, since now, in its appeal to the powerful method of proof by contradiction, the analytic would include all of the (potentially infinite) deductive consequences of a particular claim, many of which could not be plausibly regarded as “contained” in the concept expressed in the claim. For starters, Bachelors are unmarried or the moon is blue is a logical consequence of Bachelors are unmarried—its denial contradicts the latter (a denial of a disjunction is a denial of each disjunct)—but clearly nothing about the color of the moon is remotely “contained in” the concept bachelor. To avoid such consequences, Katz (e.g., 1972, 1988) went on to try to develop a serious theory based upon only the initial containment idea, as, along different lines, does Paul Pietroski (2005, 2018).
They immediately continue (and then per Conifold's comment):
One reason Kant may not have noticed the differences between his different characterizations of the analytic was that his conception of “logic” seems to have been confined to Aristotelian syllogistic, and so didn’t include the full resources of modern logic, where, as we’ll see, the differences between the two characterizations become more glaring (see MacFarlane 2002).
The ensuing section, on Frege, contrasts the containment imagery's applicability with various "intuitively analytic(al)" propositions. I'm not sure Kant would have been moved more by lists of alleged stock examples of analytical truth/knowledge than by his technical concerns, but at any rate, if we do credit our "intuition" here, then we can take ourselves to be addressing the same property dichotomy that Kant did, and then the point is that valid disjunctive reasoning is not seen to depend on the interplay of the laws of identity and noncontradiction so much, so whereas Kant did not see anything else in saying that conceptual analysis proceeded from the identity of the subject to the "unfolded" identity of the predicate (in a subject-predicate case), for Frege, et. al., disjunctive reasoning does partake of noncontradiction without reducing to the kind of simple identifications Kant points to, here, and so if analytic(al) truth/knowledge involves the positive and negative conditions of the first two Aristotelian laws, it still will go beyond them, then.
Another angle to look at it from: Kant is using a subject-predicate logic (for the most part; he makes some prescient remarks about conditionals in e.g. the Transcendental Analytic, though). Frege explicitly is not, although I did see, I believe in a focused SEP article on Frege's notation/writing, that Frege was willing to countenance having complex expressions as subjects and "is a fact" as a universal predicate, or something along that line. (I'm not sure how exactly this reflects on Frege's "prosentential theory" of the use of the word "truth" in normal discourse, though by outward theme that theory seems to allow for "it is a fact that" to be the intended counterpart, which will then take that-clauses which might be subject-predicate in form, on pain of redundancy ("It is a fact that the princess's becoming an aardvark is a fact").) Depending on how actually important, or not, such a distinction is, then if we want to retain even an identitarian method of conceptual analysis, we will have to do something besides "extract predicates from subjects" to get at Frege-format analytic(al) truth/knowledge.