No search bar on iCloud Drive?! (web browser)

I've seen the responses in prior similar questions but I'm interested how other iCloud users are able to use iCloud for finding files when they aren't on the device that has the iCloud sync drive folder that you can access in Finder.

So I have a personal mac that has that folder. Those files are now synced on iCloud.com. I travel with a work mac and need access to those files from that device. That device is not allowed to have personal data. Now I need to access those files while away and it's impossible to find what you need though across thousands of files. I used to use Google for this and the whole structure and UI is so much simpler. I assumed Apple would have this basic basic functionality so moved everything to a central spot where I also have my photos, etc.

Interested in how others are solving for this or is it just easier to use a proper storage system and give up on Apple?

Thanks very much,

Jules