Modeling suicid rates in COVID-19 pandemy

Dear colleagues,
I am going to analyze fluence of the pandemy on suicide rates in certain regions in Europe. Firsty I plan to perform the analysis in the same manner as in the following article:
Namely, authors wrote: "We used interrupted time-series analysis to model the trends in monthly suicides before COVID-19 in each country or area within country, accounting for time trends and seasonality wherever possible. Models were fitted with use of Poisson regression and accounted for possible over-dispersion using a scale parameter set to the model’s χ² value divided by the residual degrees of freedom. We modelled the effect of time as a non-linear predictor, unless this offered no improvement beyond a linear model, in which case we used the linear model instead. Non-linear time trends were estimated by selecting the best fitting model from a series of fractional polynomial models. Seasonality was accounted for with Fourier terms (pairs of sine and cosine functions)."

I am not familiar with time series analysis and with Poisson regression. I just understand that authors used suicide rate as dependent variable and time as predictor. Time was used in "mixed" manner: as a sum of fractional polynoms and two additional components: sine and cosine functions.
I don't understand following items:
How Poisson distribution may be used in this model
How I can program this regression model: predictors and specific distribution of dependent variable. I think it is not necessary to prepare function of predictors manually. Could you please advise functions or procedures (SPSS, SAS or R - in descending order of preference) or examples of code.

Apologize for the many words and possible errors in understanding the model. I would be obliged in any help in this direction.