Is it general understanding that patterns should be updated manually
across all pages if it is updated in one page?
Yes.
Block Patterns are essentially shortcuts for adding a collection of blocks all at once. Once the blocks are inserted they exist as independent blocks just like any others. There’s no meaningful difference in the result of adding a block pattern and adding that same collection of blocks manually.
Reusable Blocks are a bit closer to what you describe, as any changes you make to them will be made everywhere the reusable block is used. These can be created by selecting a block, or blocks, and clicking Create Reusable block in Block options menu. The trouble is that any changes that you make will be applied everywhere the block is used, not just styling changes.
Template Parts are very similar to Reusable Blocks, except that they are intended for site structure and only available in the Site Editor.
There’s a good support article describing the differences here.
If you want to make styling changes for a block or group of blocks across all your existing content without making content changes to those blocks then unfortunately I don’t think that’s currently supported. The closest thing would probably be using Global Styles to support changing styles globally. If global styles are added that affect the blocks in your block pattern then the styling of all existing instances of those blocks would be updated whenever the global styles are updated.