> We will need visas if we spend more than 90 days out of 180 in the EU
That's been the case since 2014, nothing to do with Brexit.
Before Brexit:
"From 9 June 2014, all British Overseas Territories citizens (BOTCs), British Overseas citizens (BOCs), British Protected Persons (BPPs), and British Subjects (BS) will be allowed to travel visa free to the EU Schengen Area for a maximum of 90 days."
After Brexit:
"If you’re a tourist, you do not need a visa for short trips to most EU countries, Iceland, Liechtenstein, Norway and Switzerland. You’ll be able to stay for up to 90 days in any 180-day period."
All the passport categories you quoted (BOTC, BOC, BPP, BS) relate to former colonies (think the status given to inhabitants of Hong Kong after it was turned over to China).
That's been the case since 2014, nothing to do with Brexit.
Before Brexit:
"From 9 June 2014, all British Overseas Territories citizens (BOTCs), British Overseas citizens (BOCs), British Protected Persons (BPPs), and British Subjects (BS) will be allowed to travel visa free to the EU Schengen Area for a maximum of 90 days."
After Brexit:
"If you’re a tourist, you do not need a visa for short trips to most EU countries, Iceland, Liechtenstein, Norway and Switzerland. You’ll be able to stay for up to 90 days in any 180-day period."