Can I add a link to my website in a paper I'm coauthoring?
Since the OP has commented that they've never seen an example of a published paper including the URL of an author's website, here is an example of such a paper:

Local Selectivity of Orders in Central Simple Algebras, Benjamin Linowitz and Thomas R. Shemanske, Int. J. Number Theory 13 (2017), no. 4, 853-884.

Our website URLs appear with our institutional information on the last page of the paper.

By the way, here's another lesson to draw from this example: try to use email addresses and website URLs that are permanent. By the time this paper was published I had already moved to a different institution and the University of Michigan had deleted the email and web accounts I listed in the paper.