Add last modified client in deployment write API's (#7323)

## What changed?
<!-- Describe what has changed in this PR -->
- had forgotten to update + add the client who last modifies the
worker-deployment workflows via the write API's

## Why?
<!-- Tell your future self why have you made these changes -->
- versioning-3.1

## How did you test it?
<!-- How have you verified this change? Tested locally? Added a unit
test? Checked in staging env? -->
- altered existing suite of tests to now account for checking the client
when current/ramp changes

## Potential risks
<!-- Assuming the worst case, what can be broken when deploying this
change to production? -->

## Documentation
<!-- Have you made sure this change doesn't falsify anything currently
stated in `docs/`? If significant
new behavior is added, have you described that in `docs/`? -->

## Is hotfix candidate?
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be sent to the broader community? (Yes/No) -->