Avoid a data race when dealing with the lowwatermark

[misalcedo]

Description

This PR fixes a data race in #1454.
That may have been the reason we saw inconsistent results when testing the parallel gh-ost setup.

In case this PR introduced Go code changes:

• contributed code is using same conventions as original code
• script/cibuild returns with no formatting errors, build errors or unit test errors.

[Copilot]

Pull Request Overview

This PR fixes a data race issue by adding proper error handling and synchronization when processing events that update the lowWaterMark.

• Added error handling for ProcessEventsUntilDrained in the migrator.
• Wrapped the lowWaterMark update in a mutex block to ensure thread safety.

Reviewed Changes

Copilot reviewed 2 out of 3 changed files in this pull request and generated no comments.

File	Description
go/logic/migrator.go	Introduces error handling when processing event draining.
go/logic/coordinator.go	Adds mutex locking around lowWaterMark update to avoid a race.

Files not reviewed (1)

• script/test: Language not supported

Comments suppressed due to low confidence (2)

go/logic/migrator.go:1322

• The new error handling for ProcessEventsUntilDrained looks good. Ensure that downstream error handling properly addresses this returned error to maintain system stability.

if err := this.trxCoordinator.ProcessEventsUntilDrained(); err != nil {

go/logic/coordinator.go:380

• The use of a mutex to protect the update of lowWaterMark is a necessary fix; however, please verify that all other accesses to lowWaterMark (both read and write) are consistently synchronized with c.mu to eliminate any data race.

c.mu.Lock()