[SM-1384] Fix panic on re-registering logger | WASM

[Thomas-Avery]

🎟️ Tracking

https://bitwarden.atlassian.net/browse/SM-1384

📔 Objective

When creating multiple WASM clients, a panic occurs failed to initialize logger: SetLoggerError()).

Looks to be the same thing we fixed: https://github.com/bitwarden/sdk/pull/181 https://github.com/bitwarden/sdk/pull/676

⏰ Reminders before review

• Contributor guidelines followed
• All formatters and local linters executed and passed
• Written new unit and / or integration tests where applicable
• Protected functional changes with optionality (feature flags)
• Used internationalization (i18n) for all UI strings
• CI builds passed
• Communicated to DevOps any deployment requirements
• Updated any necessary documentation (Confluence, contributing docs) or informed the documentation team

🦮 Reviewer guidelines

• 👍 (:+1:) or similar for great changes
• 📝 (:memo:) or ℹ️ (:information_source:) for notes or general info
• ❓ (:question:) for questions
• 🤔 (:thinking:) or 💭 (:thought_balloon:) for more open inquiry that's not quite a confirmed issue and could potentially benefit from discussion
• 🎨 (:art:) for suggestions / improvements
• ❌ (:x:) or ⚠️ (:warning:) for more significant problems or concerns needing attention
• 🌱 (:seedling:) or ♻️ (:recycle:) for future improvements or indications of technical debt
• ⛏ (:pick:) for minor or nitpick changes

[github-actions[bot]]

Checkmarx One – Scan Summary & Details – b7817415-93cd-4073-8392-535aed965882

No New Or Fixed Issues Found

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 0% with 3 lines in your changes missing coverage. Please review.

Project coverage is 58.45%. Comparing base (ac0e029) to head (c2cc8e1). Report is 52 commits behind head on main.

Files with missing lines	Patch %	Lines
crates/bitwarden-wasm/src/client.rs	0.00%	3 Missing :warning:

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #935   +/-   ##
=======================================
  Coverage   58.45%   58.45%           
=======================================
  Files         194      194           
  Lines       13358    13357    -1     
=======================================
  Hits         7808     7808           
+ Misses       5550     5549    -1     

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[coltonhurst]

As discussed with the SM team, merging this. QA will handle testing on main prior to the future release.