In principle, an operating system should not (markedly) be slowed down when a hard drive contains more data. Data just sits on a drive, and data retrieval is not significantly slowed down if a disk is more full, unless it has become badly fragmented.
The reason you experience significant slowdown likely is due to the file indexing service Tracker. Tracker searches files and contents and indexes this in a (what can become very large, i.e. GB) database, in order to allow for quick full text search of files. (see also this Askubuntu answer).
On each start, it scans the indexed directories to look for new and changed files. These files are opened to look for text and metadata, to include in the index.
If you put a lot of data there, the next time Tracker will have a lot of work inspecting all these new files, which is likely why now you experience a relatively sluggish, hard working system with loud cooling vans.
There are three options, 1) be patient and allow the indexing to complete 2) eliminate files from being indexed and 3) disable tracker altogether.
Option 1. Be patient - it will get better
After adding your files, Tracker has to go over all these files and retrieve their metadata in order to index them for quick search later. For many files, that will take significant time, during which your processor will be heavily used to an extent that - depending on your processor power - you experience a more sluggish system. You typically will hear the cooling van turning.
This indexing only proceeds once, and is repeated only when a file has changed. Still, after starting up the computer, Tracker scans all files to re-index these that have changed. That means that you still can expect high processor use shortly after startup for up to several minutes.
Option 2. Restrict the files that are indexed
Head to "Settings" - "Search". The button "Search Locations" allows to turn off the search of Pictures.
Side effects:
You cannot anymore locate photo's using Search in activities overview;
The application Gnome Photos, if you use that, will not anymore work for these photo's. Other photo management applications do not use Tracker and will be unaffected.
Option 3. Disable tracker
Tracker cannot be removed from your system, but it can be fully disabled.
Side effects
You cannot anymore search for files in Activities overview
In Files, file search by name will continue to work as well as before. However, full search will not anymore work.
In Files, the feature to mark favorite files with a star will not work anymore.
Gnome applications like Gnome Photo's, Documents or Music (not installed by default in Ubuntu) will not work.
For me personally, disabling tracker is one of the first actions after a fresh install.