You must enter both forms.
"At the end of 2022 I received a 1099-R with a distribution code H in the box 7, and gross distribution in box1"
The code-H Form 1099-R is reporting a rollover from the Roth 401(k) to a Roth IRA. It does not report anything about the In-plan Roth Rollovers that you did.
"But the Gross contribution amount in box 1 appears to include box 5 roth contribution (of case A) in this form besides the tax-deferred contribution."
In-plan Roth Rollovers and rollovers from the traditional 401(k) to a traditional IRA are both reported with code G, so all of these are properly combined on the single code-G Form 1099-R. Box 2a should show a taxable amount of $0 as long as the In-Plan Roth Rollovers were immediate so that there was no investment gain that would be taxable upon rollover to the Roth 401(k). Even though only a portion of these Form 1099-R represents the In-plan Roth Rollovers, indicate that you rolled the money over to a Roth 401(k). (TurboTax actually ignores this answer because the reporting is no different than for a rollover to a traditional IRA.) Be sure to answer No, when asked if this money was rolled over to a Roth IRA, that rollover is handled when you enter the code-H Form 1099-R.
Line 5a of Form 1040 will properly show the combined gross amounts of the two Forms 1099-R. Line 5b should show $0 (assuming $0 in box 2a of the code-G From 1099-R) and should have the notation "ROLLOVER" next to the line.
