I bought these:
Wathai Receiver DVR Xbox TV Box... https://www.amazon.com/dp/B07R659J8Z?ref=ppx_pop_mob_ap_share
Amazon Basics USB Type-C to USB... https://www.amazon.com/dp/B01GGKYXVE?ref=ppx_pop_mob_ap_share
You can’t hear the fan. The trashcan sits on top and the usb-c powers the fan.
I would wait to buy. You may not have issues like some have had. Heat was a problem for me, the fan has helped. Others didn’t see any benefit. The most important thing with these things are placement in your house. No amount of fans will fix crappy location. Also use your own router and turn off the WiFi on the gateway. Run it for a while then assess for heat issues.
You can't do that for any USB device, no. You're looking for something that can be connected to a USB HID device (keyboard, mouse, etc) and transmit that as a Bluetooth HID (for BT Classic) or HID over GATT (for Bluetooth LE) signal.
I'm seeing DIY devices (like this HID relay, here) that claim to be capable of this, but nothing that's readily availavle for sale. This kind of device would also be a bit impractical since, like you pointed out, it would still need a power source for both itself and to provide 5V power to the keyboard.
As others have said, you might have more luck with using a USB On-the-Go adapter (they're not called that anymore) a C-to-A receptacle adapter, like this one from Amazon. It's also a more flexible solution than some hypothetical USB HID to Bluetooth HID adapter, because you can also use this one to plug in USB pendrives, USB speakers, USB MIDI pianos and anything else that doesn't use HID to communicate. I know you've already tried one, and it's surprising that it didn't work, because I can tell you it works just fine plugging a mouse and keyoard on my Samsung phone.
I already have this in my car: -Anker 2 port QC 3.0 dual car charger plugged into female cigarette lighter -3ft USB flush mount extension cable
Basically, was wondering if I swap the Anker for a USB PD car charger & then add in this from the Anker PD charger to my 3ft USB extension if it would be safe. https://www.amazon.com/gp/product/B01GGKYXVE/ref=ox_sc_sfl_title_3?ie=UTF8&psc=1&smid=ATVPDKIKX0DER
With some more reading, I'm not sure if it will work properly because I think USB PD needs to be USB C to USB C.
AmazonBasics USB Type-C to USB 3.1 Gen1 Female Adapter Cable - Black https://www.amazon.com/dp/B01GGKYXVE/ref=cm_sw_r_cp_api_i_1jOuEb54E9J7R