Multiple IFs.
If HOME supports HOME->BDSP, and doesn't wipe the HT/WT data upon such an entry into BDSP, then yes, it would come into play.
Same thing for SV:
If SV supports HT/WT, and doesn't wipe HT/WT if HOME supports HOME->SV, then yeah it'll come into again.
Do notice how there's multiple IFs involved.
Just because HOME doesn't wipe HT/WT currently, doesn't mean it won't when entering future games.
Another if would be if SV even decides to support + display it.
HOME wiping HT/WT when entering future games:
As much as it doesn't do so right now, we cannot guarantee it won't in the future.
SV supporting HT/WT:
As much as it seems SV is built on PLA's engine, we can't guarantee the support.
SWSH was built on LGPE's engine and it didn't support HT/WT displays.