And this approach actually works for inland waters since NOAA predictions are accounting for geographic effects. (e.g. the tide in Seattle is drastically different in timing and magnitude from the Pacific Coast)
NOAA publishes the harmonic coefficients for each tide station, so if you hard code those constants into your program you should be able to generate accurate tide predictions. I looked into it a bunch before it started to feel less fun and more like “real work”.
https://tidesandcurrents.noaa.gov/about_harmonic_constituent...