Is charging of interest inherently rent seeking? Is the real interest rate component of interest (excluding default risk premium, etc) inherently rent seeking?

The real interest rate is typically considered to repay the opportunity cost of lending money, however, note that there is some degree of circularity in this definition: if charging of interest were prohibited on grounds of being rent-seeking, then the opportunity cost of lending would be less. So the question remains.
rent is about uncompetitive markets. In very competitive banking sector, interest will still exist. So it's not rent seeking. If laws forbide charging real interests, no private bank would be on business.

If you look at Investopedia for "Economic rent", you find:


  "Economic rent" is a term that defines an amount of money earned that exceeds that which is economically or socially necessary. This can occur, for example, when a buyer working to attain a good or service that is considered exclusive makes an offer prior to hearing what a seller considers an acceptable price. Market imperfections thus lead to the rise of economic rents; it would not exist if markets were perfect since competitive pressures would drive down prices. Economic rents should not be confused with normal profits or surpluses that arise in the course of competitive capitalist production. This term also differs from the traditional use of the word "rent," which applies to payments received in exchange for temporary use of a particular good or property, such as land or housing.


Notice: "Market imperfections thus lead to the rise of economic rents; it would not exist if markets were perfect since competitive pressures would drive down prices. "

Bill's definition is the "old version", which is not what you mean by "rent".

https://www.investopedia.com/terms/e/economicrent.asp