fix(amazonq): Add debug logging to listRegionProfile and increase cache TTL to 60s

[chungjac]

Problem

• need more logging

Solution

• log requestid for listAvailableProfiles
• some more logs
• cache expiration from 60 minutes to 1 minute

Next steps

• merge and give customer build to use. they will use it and report back the logs

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[github-actions]

• This pull request modifies code in src/* but no tests were added/updated.
  • Confirm whether tests should be added or ensure the PR description explains why tests are not required.
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