chore: improve fault proof contracts upgrade flow

[fakedev9999]

Improves fault proof contracts upgrade flow by:

1. removing the private key requirement for dry run
2. adding missing requirements in the doc.

[github-actions]

Metric	Value
Batch Start	9,557,343
Batch End	9,557,348
Witness Generation (seconds)	0
Execution Duration (seconds)	16
Total Instruction Count	337,060,965
Oracle Verify Cycles	30,347,090
Derivation Cycles	241,579,410
Block Execution Cycles	7,287,733
Blob Verification Cycles	23,288,881
Total SP1 Gas	529,393,935
Number of Blocks	5
Number of Transactions	5
Ethereum Gas Used	230,540
Cycles per Block	67,412,193
Cycles per Transaction	67,412,193
Transactions per Block	1
Gas Used per Block	46,108
Gas Used per Transaction	46,108
BN Pair Cycles	0
BN Add Cycles	0
BN Mul Cycles	0
KZG Eval Cycles	0
EC Recover Cycles	0
P256 Verify Cycles	0

[Farhad-Shabani]

👌🏻