Colour all over my sheets...

Brother is a holdout in their continued use of corona wires when everyone else has moved onto a PCR-based design. The only ones left outside of Brother are legacy designs with consumable availability due to contractual issues where it cannot be switched to a PCR. Usually, when this occurs on Brother printers, it's either the toner carts or the imaging drum due to a bad or dirty corona wire.

Clean the corona wires on all 4 drum units, then test again. Once you test it and the issue remains, you can change the offending toner carts to isolate a faulty toner or replace the offending drums. Depending on whether you bought aftermarket/reman or OEM drums, the drums you purchased may have a bad corona wire; it happens with the third-party ones, even after they've been perfected 95%+ of the time due to the printer being out on the market so long.

If that isn't it, then I would suspect the transfer belt. I know when this happens on HP lasers, there's usually toner trapped in the waste toner disposal path, and you can either take apart the transfer belt or replace it to fix the issue. It doesn't seem to affect transfer belts like the Canon and Lexmark belts (only capped on the exposed side) as often, but it seems to affect HP and Brothers with the dual cap design where both sides have a plastic cap.