Brawls in specific don't worry about type-matching. The matchmaking metric for Brawls is "# of Wins" for the current Brawls "sprint".
Brawls don't tend to linger so while you might have a tough matchup on round the next one will always be different.
In a hypothetical situation, you could have four ships that aren't in a division enter the Matchmaker at the same time. They are:
Baltimore (US Cruiser - Radar)
Anchorage (US Cruiser - Smoke)
Edinburgh (UK Cruiser - Radar)
Edinburgh (UK Cruiser - Smoke)
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In Randoms, the Matchmaker would seperate each team to have 1 US Cruiser and 1 UK Cruiser each, because Randoms will try to balance Nation/Type.
You could get this lineup:
Team 1
Baltimore (US Cruiser - Radar)
Edinburgh (UK Cruiser - Radar)
Team 2
Anchorage (US Cruiser - Smoke)
Edinburgh (UK Cruiser - Smoke)
The Random Matchmaker does not account for consumables, so Team 1 could have two Radar Cruisers while Team 2 does not. Or it could be the other way around, or it could be a mixture. The Matchmaker is only focused on Nation/Type being even if able.
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In Brawls, you might get all four Cruisers on one side while having 4 other types on the other. Type-matching is not part of the Brawls matchmaker. "# of Wins" is how the Matchmaker tries to build a team.
Every ship is balanced to its "slot" on the roster. A ship with Radar will have other areas where it is lacking so that the overall whole totals to an expected amount of power.
Ideally, a Tier 9 Cruiser should be equatable to another Tier 9 Cruiser. There will always be some amount of variance due to the game being asymmetrical, but ships are balanced against the others that they come into contact with. Consumables can be play-defining in their use, but the overall package of the ship determines its capability and gameplay.
I mention "Slot" because there is not always direct matching of ship types so it's more about having a "slot" or "spot" on the team. Brawls expressly do not type-match, so it's more about each player on the team having an expectation of capability.
You are correct that balancing is quite hard with so many variables in play. We have a multi-month process of live testing to find out how the ships perform. We make tweaks to aim for metrics to be hit, and we do factor for play capability by breaking the data out across accounts by win-rate.
If you want to learn about our balancing process, we did make a video:
devtrackers.gg