Macropads are a whole big thing in the mechanical keyboard community. You can get one that runs QMK, you can put encoders on them, have many layers, etc.

https://mechwild.com/product/murphpad/

https://knob-goblin.com/

https://github.com/dekuNukem/duckyPad

https://www.gboards.ca/product/faunchpad

It's also worth looking into small ortholinear boards where you can do the same things, but the form factor is more horizontal or has more keys.

https://mechwild.com/product/big-dill-extended-bde/

https://www.gboards.ca/product/butter-stick-limited-edition

https://github.com/nicinabox/lets-split-guide

You could do it with like an Arduino and any kind of button. There are tons of examples of using an Arduino to run a keyboard's firmware.

Another project i've done was with a Rasberry pi. A benefit of that would be that the system is self contained. Their Python GPIO library is one of the easiest i've ever worked with and you could have it easily launch Chrome or Firefox programmatically and play audio without a monitor.

MAX Falcon-8. $50 assembled, $40 DIY (some soldering, but easy). Add a few dollars more for switches and you provide the keycaps. 8 programmable keys. I wouldn't call it cheap but it's definitely cheaper than the author's option. I got one somewhere; it is nice but I don't really use it much nowadays.

I've looked but they don't seem to exist. Closest I found was MIDI pad controllers (around £40) but I'm not sure about the ergonomics of using a pad as a button.

I gave up and went with an Mbed board instead. It has the advantage that you can program key sequences without writing any host software. I use it with Audacity.

Simplest solution would be to just remap keys you don't use with something like Autohotkey.

If you want a separate keypad a cheap solution would be to use any old keyboard and then remap that one specifically with a tool like http://www.hidmacros.eu/whatisit.php (optionally you can paint or add labels to the keys to make it easier to use).

I think simple website (with all your favorite channel as big black button) and pin it to taskbar would solve your problems

Icons on desktop