Personally I have my catalog and images on an external.. Well two actually, one is an SSD with the catalog and recent years folders. The other is a 24TB drive with older photos, still in Lightroom. I simply couldn't fit them on an internal, so I have to use external drives. The catalog could be on my internal, but sometimes I'll take the SSD with me to work away from my desk.
Lightroom Classic catalogs the files you import, but they must be connected to do full work on. Yes, you can use Smart Previews as @F. McLion says and that will allow you to get basic edits done, but not at a detailed level. You simply have to keep the drive connected to work on the file properly. This would be true of most programs. You could use Lightroom, where the files are stored in the cloud, but that's charged in 1TB increments at $10 per month. If you never go over 1TB you're fine on the base subscription, but more means more outgoings.
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