The ones I mentioned above can be of usefulness, as they are good examples of the mainstream:

https://mitpress.mit.edu/books/economics-growth

https://press.princeton.edu/books/hardcover/9780691132921/introduction-to-modern-economic-growth

I would say the following:

-in general, it is not a good idea to have a state variable in a utility function, because, in the long run, this variable will dominate everything else

-but there are models of habit formation in which there is a stock of habits (depending on past consumption) included in the utility function

-there are also models in which the discount rate depends on wealth

-in human capital driven endogenous growth models, if there is disutility of leisure, you need to scale that disutility by human capital otherwise it would be negligible in the long-run

See the article

https://www.google.com/url?sa=t&source=web&rct=j&url=https://iopscience.iop.org/article/10.1088/1742-6596/1388/1/012033/pdf&ved=2ahUKEwjsnI38xebwAhUTwzgGHdM-BSAQFjAMegQIFRAC&usg=AOvVaw1pty-my2XHi_a_0uZPsPPB