How is the B737NG Autopilot controlling pitch?
This is from the B737NG airplane manual. Boeing doesn't offer the technical drawings in the pilot manuals, one would have to have access to the maintenance manuals. Boeing is very sticky about their material being published on the internet.

Autopilot Flight Director System (AFDS)
The AFDS is a dual system
consisting of two individual flight control computers (FCCs) and a
single mode control panel. The two FCCs are identified as A and B. For
A/P operation, they send control commands to their respective pitch
and roll hydraulic servos, which operate the flight controls through
two separate hydraulic systems.

This is a brief explanation of an autopilot system such as on the B737 from this website.

Aircraft with hydraulically actuated flight control systems have
autopilot servos that are electro-hydraulic. They are control valves
that direct fluid pressure as needed to move the control surfaces via
the control surface actuators. They are powered by signals from the
autopilot computer. When the autopilot is not engaged, the servos
allow hydraulic fluid to flow unrestricted in the flight control
system for normal operation. The servo valves can incorporate feedback
transducers to update the autopilot of progress during error
correction.