You could start with a $70 AIYAMA A-07 and at least listen to them.
It is not a bad amp… but it is just an amp…
So one could do the TV or the CD or… just not TV and CD.
And they peddle those amps on Amazon.
Then you can listen and take your time finding something if you need it.
Many TVs will do internet and get to YouTube, and that amp will not be holding you back in SQ.
If you had some high def sound streaming source, then maybe the SQ would be better with something else. It probably would, but the speakers likely have more distortion than the amp.
So I would be more inclined to suggest the AIYAMA and a streamer running Roon or similar… but you would need some switch or pre amp to move between streamer and TV.
Really just try the amp if the TV can find a way to get itself connected to YouTube… and call it a day. (IMO)