Type count from cache if possible

[joente]

Description

When cache is available, type_count() can use this instead of counting the instances by itself.

Type of change

• Improvement

How Has This Been Tested?

• Test type (update).

Checklist:

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• New and existing unit tests pass locally with my changes