PIP(Picture in Picture) is a Multitasking feature supported by iOS. You can change the subtitle style of the PIP mode in the iOS Settings app.
1

Go to Settings app > General > Accessibility.
2

Tap Subtitles & Captioning of MEDIA.
3

Tap Style.
4
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Tap Create New Style….
5

After you set up a new style, tap Save.
Default
Apply the Style

BACKGROUND > Opacity > 0%,
ADVANCED > Text Edge Style > Drop Shadow