test: Small mempool_compatibility.py cleanups #36511

After #36294:

• The MiniWallet mode can be dropped (using the default), now that all nodes support taproot.
• The sync_fun=self.no_op can be dropped (using the default sync), if the node connection is done earlier.
• A check for the unbroadcast set can be added, now that all nodes support persisting the set.

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External sites

• Code coverage & benchmarks: https://corecheck.dev/bitcoin/bitcoin/pulls/36511
• Ralph review <img src=https://review.fish.foo/assets/bitcoin/bitcoin/36511.png alt="Ralph review status"> https://git.fish.foo/bitcoin/bitcoin/pulls/36511#author-ralph

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🚧 At least one of the CI tasks failed. _{Task lint: https://github.com/bitcoin/bitcoin/actions/runs/38372223938/job/115211755213} _{LLM reason (✨ experimental): CI failed because Ruff found an unused MiniWalletMode import in test/functional/mempool_compatibility.py.}

<details><summary>Hints</summary>

Try to run the tests locally, according to the documentation. However, a CI failure may still happen due to a number of reasons, for example:

• Possibly due to a silent merge conflict (the changes in this pull request being incompatible with the current code in the target branch). If so, make sure to rebase on the latest commit of the target branch.

• A sanitizer issue, which can only be found by compiling with the sanitizer and running the affected test.

• An intermittent issue.

Leave a comment here, if you need help tracking down a confusing failure.

</details>

tACK fae8a8fd3cc5c511191a18665a731195a9ac228d

Tested locally against v31.0 (x86_64-linux-gnu), it passes. I also verified the new unbroadcast assertion catches a regression, clearing unbroadcast_txids before it's written in DumpMempool makes the test fail at the new assert_equal (not(False == True)), while the earlier asserts still pass, including both txs being in the old node's mempool.

Code review ACK fae8a8fd3cc5c511191a18665a731195a9ac228d