supersedes https://github.com/paritytech/parity-bridges-common/pull/2873

Draft because of couple of TODOs:
- [x] fix remaining TODOs;
- [x] double check that all changes from
https://github.com/paritytech/parity-bridges-common/pull/2873 are
correctly ported;
- [x] create a separate PR (on top of that one or a follow up?) for
https://github.com/paritytech/polkadot-sdk/tree/sv-try-new-bridge-fees;
- [x] fix compilation issues (haven't checked, but there should be
many).

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Co-authored-by: Adrian Catangiu <adrian@parity.io>