esc_url is the correct function to escape links -> https://codex.wordpress.org/Function_Reference/esc_url – if it’s not working correctly then double check the actual output of your variables to make sure they are in fact links.
But selling links in your themes via “sponsored” links is not something I would ever recommend anyone doing which from the code it looks like you are doing. “Powered by” should be followed by “WordPress”. And maybe even “developed by Your Name” – but selling links in themes just makes them look spammy and untrustworthy (my 2 cents).