refactor(tests/integration): Port distribution integration tests to server v2 #75528

Job	Run time
test-clientv2	35s
test-integration	9m 5s
split-test-files	15s
test-core	34s
test-sim-nondeterminism	4m 36s
test-system	13m 11s
test-coretesting	25s
test-depinject	45s
test-errors	41s
test-math	42s
test-schema	45s
test-schema-testing	39s
test-collections	40s
test-collections-protocodec	34s
test-confix	37s
test-cosmovisor	43s
test-hubl	39s
test-indexer-postgres	33s
test-log	38s
test-orm	47s
test-simapp	2m 0s
test-simapp-v2	5m 31s
test-store	44s
test-store-v2	1m 53s
test-x-accounts	40s
test-x-accounts-base	30s
test-x-accounts-lockup	25s
test-x-accounts-multisig	25s
test-x-circuit	41s
test-x-distribution	40s
test-x-evidence	45s
test-x-feegrant	48s
test-x-nft	42s
test-x-params	39s
test-x-protocolpool	39s
test-x-tx	36s
test-x-authz	37s
test-x-bank	41s
test-x-epochs	36s
test-x-gov	45s
test-x-group	46s
test-x-mint	36s
test-x-slashing	45s
test-x-staking	1m 42s
test-x-upgrade	46s
test-x-consensus	46s
tests (00)	8m 22s
tests (01)	3m 36s
tests (02)	4m 4s
tests (03)	4m 17s
repo-analysis	2m 23s
	1h 25m 44s

Provide feedback