According to previous discussions, the size of the catalog should have no performance impact on Lightroom. It is just a database. It might speed up the backup process. But it's doubtful that it would provide any performance improvement. A single catalog provides for much more efficient file management.
Should I be splitting my library into yearly catalogue so that each catalogue only contains 100k photos?
No!!! This is an absolutely horrible idea, it has huge amounts of drawbacks, and there's no reason for it.
What kind of performance penalty would I face if I didnt do this?
No penalty that I know of (except that it will take a long time to back up, and this is usually done overnight) People run very large catalogs now without performance penalties.
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The catalog is a modern database file. As such it does not have performance issues when it gets big.
As a general rule, one catalog is better than multiple catalogs.
In reality, it all depends on how you are using you photos.
For example, my personal photos are all in one catalog, for however many photos that comes to.
For my sports shooting and event shooting, I use one catalog per year for each. For each match/event, the photos are triaged, sorted, deleted, processed, uploaded, and archived. After the photos are archived and uploaded to my website, they are never touched again. At the end of the year, that catalog is archived. The catalog and photos are then removed from my working hard drives.