Annotate checklocks on mutex protected fields
Annotate checklocks on mutex protected fields

...to catch lock-related bugs in nogo tests.

Checklocks also pointed out a locking violation which is fixed
in this change.

Updates #6566.

PiperOrigin-RevId: 397225322

google/gvisor,google/gvisor,google/gvisor,google/gvisor,google/gvisor,google/gvisor,google/gvisor,google/gvisor