First, let me confirm and agree with the OP that the Hebrew text of 2 Sam 21:8 has "Michal". What do most versions give "Merab"?
This question is answered by (among many others) by Ellicott when he writes:
The text has Michal instead of Merab; but this must be an error of the
scribe, since it was Merab, not Michal, who was married to “Adriel the
Meholathite” (1 Samuel 18:19), and Michal was childless (2 Samuel 6:23).
The English phrase “brought up for” is taken from the Chaldee; the
Hebrew, as noted in the margin, is bare to.
The Cambridge Commentary has more details:
he five sons of Michal … whom she brought up for Adriel The Heb. text can only mean whom she bare to Adriel. But it was Merab, not
Michal, who was married to Adriel (1 Samuel 18:19). Consequently we
must either read Merab for Michal, or take the explanation given in
the Targum and adopted by the E. V.: “the five sons of Merab, (whom
Michal the daughter of Saul brought up), whom she bare to Adriel.”
The Pulpit commentary is similar:
Verse 8. - Michal. It was Merab who became the wife of Adriel the
Meholathite (1 Samuel 18:19). Michal was childless (see 2 Samuel
6:23). Whom she brought up for. This is one of the many cases of
untrustworthiness in the renderings of the Authorized Version. We have
noticed a very flagrant instance before in 2 Samuel 5:21. The object
of these mistranslations is always the same, namely, to remove some
verbal discrepancy in the Hebrew text. The Hebrew says here "five sons
of Michal, whom she bare to Adriel;" but Michal never bore a child,
therefore something must be substituted which will save the Hebrew
from this verbal inaccuracy, and Michal must be represented as having
taken Merab's place (perhaps at her death), and been foster mother to
her children. This explanation is, it is true, taken from the Jewish
Targum; but the Targum never professes to be an exact translation, and
constantly perverts the meaning of the plainest passages for
preconceived reasons. 2 Samuel 21:8
