Core: Add Merkle Tree generation to the /analyze endpoint payload

[EDOHWARES]

Include tree root calculations in the backend JSON response if requested.

[Chigybillionz]

@Chigybillionz has applied to work on this issue as part of the Stellar Wave Program's 5th wave.

Hi, I’ve reviewed this issue and I’m confident I can fix it. I’d like to take it on.

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Congratulations, @Chigybillionz! 🎉 Your application was accepted by the repo's maintainers, and the issue is due on June 2, 2026.

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