If you're using Python, statsmodels is good for their ARIMA models. You'll need to read up a bit on the theory beforehand though.

https://otexts.com/fpp3/

Yep stasmodels and pandas are OP here

sktime. I have been using this in my projects and is quite good and is still developing

but it is based on statsmodels so statsmodel is good as well

Here is a comparison of ARIMA vs Prophet, that used Python’s StatsForecast Library.

The classic methods like smoothers/arima/theta can be found in libraries like sktime, pycaret, and darts. I kind of prefer the new pycaret stuff coming out.

"similar to FBProphet" in what way? The decomposition of trend/seasonality/exogenous or the simplicity of the API? If you just want more firepower you could try PmdArima for auto-arima, it does ok and will outperform prophet more often than not and it is an automatic procedure which is nice.

If you are feeling adventurous you could try some of my packages: ThymeBoost or LazyProphet. ThymeBoost is interesting as it is gradient boosting around time series decomposition. So you will still have the trend/seasonality decomposition but with more exotic methods. LazyProphet is just some feature engineering for time series fed into Lightgbm but it tends to perform well enough. Both tend to outperform fbprophet although that generally isn't too hard to do and they both have automatic fitting procedure that performs ok.