[backport][HLSTree] Set period duration also with live stream

[CastagnaIT]

Description

bp #1793

Motivation and context

How has this been tested?

Screenshots (if appropriate):

Types of change

• Bug fix (non-breaking change which fixes an issue)
• Clean up (non-breaking change which removes non-working, unmaintained functionality)
• Improvement (non-breaking change which improves existing functionality)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that will cause existing functionality to change)
• Cosmetic change (non-breaking change that doesn't touch code)
• None of the above (please explain below)

Checklist:

• I have read the Contributing document
• My code follows the Code Guidelines of this project
• My change requires a change to the Wiki documentation
• I have updated the documentation accordingly