Can I restrict my team to only see a part of the board?

No. Kanban Tool access is assigned at the board level, and sharing a board means sharing everything within it: all columns, all swimlanes, and all tasks.

You can control which users see specific boards and how much they can do within them, but you cannot control which parts of a board are visible or hidden.

If some of your team members should not see specific information, please place it on a board that is inaccessible to them.

But if it is simply a matter of improving board readability, each user can filter the board using their chosen criteria (for example, by team member assignment or card type) reducing visual noise and the number of displayed tasks.

Furthermore, users can search for specific tasks across all boards to focus only on what matters to them at a given moment.
Enterprise plan subscribers can also create individual, sortable task lists from multiple boards to simplify their work planning.