Covid new cases and death

#1
Real life question:

I live in a country in the world with high number of cases. The state where I live has been relatively better when it comes to the number of deaths but daily cases has been high.
An interesting observation is in the past 65 days or so the number of deaths have been consistently between 20-30 where the daily cases have varied from 2700-11800
This makes me think if the government is under reporting the number of deaths.
The test positivity rate (positive covid cases in 100 samples) in the last 65 days first increased and then reached a peak and now it seems to be gradually decreasing as per government data.
I have the data for number of deaths for the 65 days as well as the daily new cases for the past 65 days. Using these two sets of data what should I measure to see to make any inference at all to see if there is serious statistic anomalies or discrepancies.

Govt hasn't made any serious policy changes like lockdowns which would decrease the new cases drastically nor they have improved the medical facilities drastically in the last 2 months (most of such parameters remain the same)

Any pointers to make any statistical analysis using the 2 sets of data that I have mentioned above

PS: I haven't done any complicated stats in my life in the last 9 + years or so, so struggling to even start off