refactor!: remove broadcast mode block

[julienrbrt]

Description

Closes: #12167

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Author Checklist

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I have...

• included the correct type prefix in the PR title
• added ! to the type prefix if API or client breaking change
• targeted the correct branch (see PR Targeting)
• provided a link to the relevant issue or specification
• followed the guidelines for building modules
• included the necessary unit and integration tests
• added a changelog entry to CHANGELOG.md
• included comments for documenting Go code
• updated the relevant documentation or specification
• reviewed "Files changed" and left comments if necessary
• confirmed all CI checks have passed

Reviewers Checklist

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I have...

• confirmed the correct type prefix in the PR title
• confirmed ! in the type prefix if API or client breaking change
• confirmed all author checklist items have been addressed
• reviewed state machine logic
• reviewed API design and naming
• reviewed documentation is accurate
• reviewed tests and test coverage
• manually tested (if applicable)

[codecov]

Codecov Report

Merging #12659 (e64760f) into main (4fe7797) will decrease coverage by 1.24%.
The diff coverage is 28.00%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #12659      +/-   ##
==========================================
- Coverage   55.87%   54.63%   -1.25%     
==========================================
  Files         646      671      +25     
  Lines       54895    57693    +2798     
==========================================
+ Hits        30675    31518     +843     
- Misses      21762    23635    +1873     
- Partials     2458     2540      +82     

Impacted Files	Coverage Δ
baseapp/grpcrouter.go	90.00% <ø> (ø)
baseapp/grpcrouter_helpers.go	25.00% <ø> (ø)
baseapp/grpcserver.go	1.72% <ø> (ø)
baseapp/msg_service_router.go	85.29% <ø> (+4.41%)	⬆️
baseapp/options.go	67.92% <0.00%> (-0.60%)	⬇️
client/broadcast.go	54.54% <ø> (+2.99%)	⬆️
client/cmd.go	57.73% <ø> (ø)
client/config/toml.go	55.55% <ø> (ø)
client/context.go	54.49% <ø> (-1.79%)	⬇️
client/flags/flags.go	19.35% <ø> (-0.32%)	⬇️
... and 231 more

[amaury1093]

I love PRs that remove code!

[alexanderbez]

🚀

[julienrbrt]

back to this, sorry for the delay

[alexanderbez]

Great job on pushing this over the finish line @julienrbrt

bravo 👏