I have learned some attribution models such as Campisi. It decomposes the return of bond into treasury return, spread return, and coupon return. It works like: $$r = y\times dt - D \times dy_\text{treasury} - D \times dy_\text{credit}$$
Can an interest rate swap be decomposed in a similar way?
You can decompose swap returns this way although I would argue that you should think more in terms of risk factors. For most any fixed income instrument (and especially for swaps), we often break exposure into three types of yield curve movements which explain the most variation, aka the Litterman and Scheinkmman (1991) factors:
In addition, you have credit concerns since interbank rates are not risk-free; thus, you could look at a short-term credit spread like the TED spread (which can help indicate different states of the economy) and a longer-term credit spread like the Moody's yield of 10-year Baa corporates over 10-year US Treasuries.
Your coupon return is easy to calculate; however, you should also calculate a component for change due to rolling down the curve (as noted in a comment). Finally, you might also account for when certain cashflows roll past more liquid points on the curve to account for liquidity premia.
