There are potentially different sizes being discussed, with different importance:
The size of the Lightroom Classic catalog file (the one that has the filename extension .lrcat)
The size of the Lightroom Classic previews cache file (the one that has the filename extension .lrpreviews)
If the size of the catalog file is literally 135MB, that is tiny, and of no concern. Many of us have catalogs that are several GB in size. (A gigabyte, or GB, is 1000 megabytes or MB.)
Keep in mind that catalog loading time, even with a very large catalog, should not be an issue on a recent computer. It should be quick. But there is one thing about your installation that’s different: You have put the catalog folder on OneDrive. That means OneDrive is probably constantly syncing any changes to it with its copy on the cloud server. And that means, every time you do anything that changes the catalog database or the previews file, OneDrive will want to sync it to the cloud. This is sort of OK on a fast Internet connection, some people do it and it works most of the time (but is not recommended). But if you’re combining OneDrive sync with a slow Internet connection, and it’s going to keep trying to sync all of this data back and forth all the time, the demands it makes on your slow Internet connection might be an impractical way to store your catalog.
The size of the previews cache is not listed, it’s missing from the screen shots. But it can typically become many times the size of the catalog file. If we’re looking for a file that’s too large and causing delays, it could be the previews cache. Fortunately, the previews cache is expendable., so if its size is intolerably large, just delete it and Lightroom Classic will automatically start rebuilding it, so it will start out small again. You can also use the new option in Catalog Settings that limits how large the previews cache is allowed to be.
When Lightroom Classic is used normally, with a catalog folder on local storage (not relying on the Internet), the catalog folder (because it contains the previews cache) is performance-critical and best stored on the fastest local storage you have. But if it’s always having to wait to be cloud-synced over a slow connection, well, that is the opposite of ideal.
If the Internet connection is slow, it will be most practical and reliable to use Lightroom Classic as designed: Storing the catalog on a fast local volume, such as your computer’s internal storage, or if there isn’t room, on a fast external volume (over fast USB or Thunderbolt) like I do. Lightrom Classic was designed as a local application so has almost no performance optimizations for cloud-synced use (except for its own Lightroom cloud sync feature).
For context, Adobe has other services that are better optimized for cloud sync, such as Lightroom (the non-Classic, cloud-based one), and Photoshop/Illustrator/InDesign cloud documents. The reason cloud documents work well is because when you make a change, they can sync only the changed bits — they don’t have to re-sync entire huge documents.
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