test(dot/parachain/backing): Write integration tests

[axaysagathiya]

NOTE

These sub-issues are not ready, and I have been adding extra details to each one.

• I will improve the title of issues
• add tags to all of them
• add the description of the tests

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Sub issues

• [ ] #4029
• [x] #4003
• [ ] #4007 (we haven't issued an invalid statement before.)
• [ ] #4008
• [ ] #4004
• [x] #4005
• [ ] #4006
• [ ] #4009
• [ ] #4010
• [ ] #4011
• [ ] #4012
• [ ] #4013
• [ ] #4014