fix: pass through broadcast mode for signing with amino flag (#10510)

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## Description

Fixes signing with amino flag.

Closes: #9671 

<!-- Add a description of the changes that this PR introduces and the files that
are the most critical to review. -->

Passes through broadcast mode flag value.

---

### Author Checklist

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- [x] included the correct [type prefix](https://github.com/commitizen/conventional-commit-types/blob/v3.0.0/index.json) in the PR title
- [ ] added `!` to the type prefix if API or client breaking change
- [x] targeted the correct branch (see [PR Targeting](https://github.com/cosmos/cosmos-sdk/blob/master/CONTRIBUTING.md#pr-targeting))
- [x] provided a link to the relevant issue or specification
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- [ ] included the necessary unit and integration [tests](https://github.com/cosmos/cosmos-sdk/blob/master/CONTRIBUTING.md#testing)
- [ ] added a changelog entry to `CHANGELOG.md`
- [ ] included comments for [documenting Go code](https://blog.golang.org/godoc)
- [ ] 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](https://github.com/commitizen/conventional-commit-types/blob/v3.0.0/index.json) 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)

x/auth/client/cli/tx_sign.go

@@ -263,6 +263,11 @@ func makeSignCmd() func(cmd *cobra.Command, args []string) error {
 			return err
 		}
 
+		bMode, err := f.GetString(flags.FlagBroadcastMode)
+		if err != nil {
+			return err
+		}
+
 		var json []byte
 		if aminoJSON {
 			stdTx, err := tx.ConvertTxToStdTx(clientCtx.LegacyAmino, txBuilder.GetTx())
@@ -271,7 +276,7 @@ func makeSignCmd() func(cmd *cobra.Command, args []string) error {
 			}
 			req := BroadcastReq{
 				Tx:   stdTx,
-				Mode: "block|sync|async",
+				Mode: bMode,
 			}
 			json, err = clientCtx.LegacyAmino.MarshalJSON(req)
 			if err != nil {