I like the idea of restricting a settlement to a biome rather than a radius. However, as you said, it might cause some problems. A possible solution is to allow certain buildings (mines, roads, 2x2 towers eventually) and activities (gather pigs, cut trees...) to be built in adjacent biomes, letting citizens gather ressources from adjacent biomes, but not live there.
A more complicated idea would be to have a specific building (a town hall) that claims a biome. When a group of settlers is ordered to settle, they build such a building, claiming the biome. When a settlement reaches a certain population, it is allowed to build another such town hall, claiming a second biome. This could again tie into districts somehow. The masklings may also be drawn to the town hall, trying to destroy it to kick the settlers out. It would also be a prime target for all kinds of upgrades and various mechanics and interface (nobles, diplomacy, early religion...).
I also like the idea of maskling tribes claiming biomes. It would make them seem more intelligent, more relatable, and it would open the possibility of peaceful interactions down the line. And/or conflict between masklings. Maybe they'll even expand under certain circumstances, one tribe gaining in power and asserving or wiping out tribes you were trading with would be a matter for concern or even war. Imagine, going out at war to save masklings!