You’re not asking too much, but you will need a server (or some way to run the software) to actually create some sort of organization, image/object/face recognition processing, etc. that is indexed and can be searched. Depending on what tasks are being run will depend on how much system resources you’ll need or what specific hardware is required to process the files.
Now, does the technology exist there to do what you are looking for without needing to get a server yourself? Yes, it absolutely does. However a lot of it can be found within Media Asset Management systems (not free) that connect to services that do the actual processing (costs extra and really not free). Like, if you wanted to search through your images and find every image with a red coffee cup in it, you could.
This also goes without saying, but if you have a single HDD with all your photos on it, the last thing you should be doing is running high I/O tasks on that HDD if that is your only copy. You should ingest those files into whatever solution you want and process it there, leaving the original intact. Ideally, duplicate that HDD and work off the duplicated data.
For the price point, Kingston DC1500M U.2. Get a dual U.2 to PCI-E x8 adapter for your mirror.
A 3.84TB single disk model should be still just a tad higher than 200 euros.