united-states
Can I cite the decision for the purposes of Issue S alone, even though
the overall decision was overruled?
Yes. This is done routinely, even by the courts themselves in their opinions.
You state the position or quote from the case that you want to use, followed by a citation to the case. And, in the citation, you further note the citation to the case overruling it and state "overruled on other grounds." See generally the current edition of The Blue Book: A Uniform System Of Citation. Almost all U.S. courts adopt the Blue Book, or a simplified citation system based upon it, as the standard for citing to legal authority in legal documents. Sometimes this is done expressly by court rule or order, and sometimes this is done by implication.
Some examples from a single case picked at random are as follows:
28 U.S.C. § 2254 is the exclusive avenue for a state prisoner to
challenge the constitutionality of his detention. White v. Lambert,
370 F.3d 1002, 1007 (9th Cir. 2004), overruled on other grounds by
Hayward v. Marshall, 603 F.3d 546 (9th Cir. 2010) (en banc),
overruled on other grounds by Swarthout v. Cooke, 562 U.S. 216 (2011).
and
Although Petitioner asserts “loss liberty interest in loss good time
credits, loss Program treatment, loss classification, loss of Pro
social living Community and the loss of working at Optical,” ECF No.
11 at 20, he has presented no facts in the First Amended Petition from
which the Court could infer that the disciplinary action affected the
fact or duration of his confinement. See Preiser v. Rodriguez, 411
U.S. 475, 500 (1973), overruled on other grounds by Heck v.
Humphrey, 512 U.S. 477, 482 (1994).
Both of these citations are from Williams v. Key, No. 2:22-CV-00081-SAB, 2022 WL 6538548, at *1 (E.D. Wash. Sept. 27, 2022), certificate of appealability denied, No. 23-35065, 2023 WL 4785509 (9th Cir. July 25, 2023).
Of course, if you can find a case supporting your position that was not overruled, you should also cite it, in addition to, or in lieu of, the case that was overruled on other grounds. This is because if a case is overruled on other grounds, the proposition to which you cited could be incorrect but was just unnecessary to address since another issue resolved the case.