🏛️Product base types: Support in the integrator

[antirotor]

Changelog Description

Integrate product base type into AYON on publishing.

Additional info

If instance has product base type defined, integrate it.

Closes #1296

[!NOTE] This requires https://github.com/ynput/ayon-python-api/pull/255 and definitely https://github.com/ynput/ayon-backend/pull/575

For more information about product base types and testing see description here https://github.com/ynput/ayon-core/issues/1297