Can you get a closeup of that sticker that says 12V on it?
You need a standard 12V barrel plug AC adapter, but I can't tell if it's center positive or center negative that you need (it's probably center positive because they're more common)
It's likely you have one lying around somewhere in your house but if you don't, something like this will probably do it.
Some console controllers had proprietary ports, so I don't think they can be directly attached to PC.
This looks like a serial port though, haven't seen it in a while, don't think newer computers have it. A quick online search shows there are Serial to USB cable available, you can give them a try. An example: https://www.amazon.com/Sabrent-Converter-Prolific-Chipset-CB-DB9P/dp/B00IDSM6BW/ref=sr\_1\_3?dchild=1&keywords=serial+to+usb+adapter&qid=1632740016&sr=8-3
What region are you in? I found an OEM listing on Amazon
If you don't need it to be official, you can probably get a third party one for cheaper.
https://www.fivebelow.com/products/24-game-card-storage-case-for-switch
You can still find them in some of the actual stores. If you can find them this is the cheapest option.
While I don't personally have the hori I have the binbok they are similar in size.
I use this case https://www.amazon.com/Fintie-Carry-Nintendo-Switch-Controller/dp/B08SWRYF5J?ref_=ast_sto_dp&th=1&psc=1
My binbok fit in the dock no problems so I don't see you having any problems with the hori.
Oh if you do decide to get the binbok joy cons a regular carrying case won't work if you want to carry your switch with binbok connected to your switch. I suggest this carrying case. It is originally made for the hori split pad pro but it works fine with the binbok.
If you aren't interested in the binboks but still want ergonomic handles I have heard great things about the Satisfye grip. They finally have the ones for the oled switch out (the oled switch is just a little bit bigger than the regular switch so the had to make newer grips), this grip uses the regular joy cons and just slips on to your switch.
I think most any glass screen protectors will work. The one I got is more expensive but really easy to install. But as I said any glass screen protector will work.
https://www.amazon.com/dp/B09JG8V83Z/ref=cm_sw_r_awdo_navT_g_MT0MNWT5JRGQY251ENGB
I have recently gotten a binbok joy pad controller (which I love) it does every thing the regular joy cons do except the amiibo, but these are ergonomic so it makes it a lot more comfortable to play handheld it also as turbo button on the back. Now what what I have heard is there are some quality control issues and you might have to return and get new ones. But I didn't have any issues with the set I got. I love it.
Right now on Amazon for the next 2 hours it is on sale for 36.99 instead of 49.99 because it is a lighting deal.
https://www.amazon.com/dp/B08ZH4XXNY/ref=cm_sw_r_awdo_navT_g_CK222A1TTPW4H824JZYX
I know this is not quite what you asked, but I invested in a clear plastic shell for my new3DSXL to hopefully avoid the paint peeling issue. I'm really happy with mine!
WD Blue 3D NAND 500GB Internal PC SSD - SATA III 6 Gb/s, 2.5"/7mm, Up to 560 MB/s - WDS500G2B0A https://www.amazon.ca/dp/B073SBZ8YH/ref=cm_sw_r_apan_i_KTEZ0KF8E0VBNNHCYVVY?_encoding=UTF8&psc=1
Would this be better?
You can get an adapter on amazon (this is the first one I found you might find one better with some searching). I've used one in the past and while there is some loss of quality, nothing too bad imo.
I personally have gotten controllers from thrift stores and occasionally collector game stores (for a lot more). Just make sure it has the OG plug not a USB plug.
The connectors are technically inside the unit, so the cartridge only has contacts which are copper plated with gold, which doesn't "rust" but can oxidize over time.
That blowing thing was actually was just a joke though. But you might like to learn of the existence of this product that can take care of that oxidation the right way. Take care!
I used these ones. Took me about 30 minutes per joycon as it was my first time doing it and wanted to be super careful.
https://www.amazon.com/Veanic-2-Pack-Replacement-Joystick-Controller/dp/B07MRJ12HX
Hmm I checked apparently that drifts too here buy this instead
No one has reported drift and it shouldn’t and even if it does it’s much cheaper