feat(all): sync state root rather than signal service's storage root

[davidtaikocha]

ref: taikoxyz/taiko-mono#15671

[codecov]

Codecov Report

Attention: 19 lines in your changes are missing coverage. Please review.

Comparison is base (738194d) 54.91% compared to head (be64dcc) 54.93%.

Files	Patch %	Lines
pkg/rpc/utils.go	0.00%	7 Missing ⚠️
pkg/rpc/methods.go	25.00%	6 Missing ⚠️
driver/state/state.go	0.00%	2 Missing ⚠️
prover/proof_submitter/proof_contester.go	0.00%	2 Missing ⚠️
prover/proof_submitter/proof_submitter.go	75.00%	1 Missing ⚠️
prover/prover.go	90.90%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #549      +/-   ##
==========================================
+ Coverage   54.91%   54.93%   +0.02%     
==========================================
  Files          44       44              
  Lines        5538     5499      -39     
==========================================
- Hits         3041     3021      -20     
+ Misses       2176     2158      -18     
+ Partials      321      320       -1     

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