Is there a unit root test that works with structural change? I only found Zivot-Andrew test but I would try another test, I do not know if the timeseries has a structural change, so I need a test that works with A break at unknown time.
Zivot Andrews tests the alternative of a one time structural break against a null of a unit root process. Variations in the ZA paper test for a change in the intercept, in the trend, or in the intercept and the trend.
ZA endogenously selects the break point based on the point in time that gives the most weight to the alternative (ie that is most against the unit root null).
It is the prominent (only?) test in the literature for an endogenously determined structural break against a unit root null.
The approach has been extended to 2 breaks (both in the intercept, both in the trend, or one of each) (Lumsdaine, R. L., & Papell, D. H. (1997). Multiple trend breaks and the unit-root hypothesis. Review of Economics and Statistics, 79(2), 212-218.
Last time I looked at the R programs available addressing unit root testing they did not address serial correlation in the way that the original papers did.
Your addendum says you want to check if the series is constant without changes. That is different from saying you want to test for a structural break against a unit root null, as a unit root process need not have an expected value that is constant. There are other tests for structural breaks that do not have a unit root process as the null hypothesis if that is what you are really after.