I can't see your images and can't figure out what they were originally supposed to be to try to recreate it.
Still
To connect a standard desktop hard drive to a PC one normally uses a so called hard drive caddy, though hard drive reader is also a term (the former being more for people that want to put their own drive in an external case, the latter basic computer repair, though I have used and continue to use the former both in my day to day life to swap around hard drives out of my pile of the things and to recover hundreds of hard drives for clients, and you can get more specialist recovery devices too if you need that sort of thing).
What formats they support varies (SATA, IDE/PATA, SAS, SCSI, PCI... though for practical purposes you will mostly want SATA these days, maybe IDE for older drives, dual SATA and IDE caddies exist and were made in large numbers), as does what link they use (some include standard USB A-B which you might more normally recognise from printers, some newer USB forms, some solder the thing directly inside the board, some will be limited to USB 2.0 or worse and some will be newer fast USB). Some will only power 2.5 inch drives as they don't need as much as some 3.5 inch ones (they tend to support 12V in which is harder to do from USB) but if they have an external power or support that size as a caddy you should be good.
I would also wonder what about your reader failed. Often times the cable it comes with or the power adapter (which might be custom) fails as such things are not really designed for hundreds of removals and insertions. I tend to solder them back up or make another but play that as you will.
