Should we account for competing risk when estimating incidence rate?

I would like to analyse a set of data consisting of patients diagnosed with Klebsiella Pneumoniae Bacteraemia. Patients may have (1) liver abscess, (2) extrahepatic manifestation or (3) no systemic manifestations. The endpoint is development of colorectal cancer (CRC).

I would like to measure the following:

(I) incidence rate of CRC and the incidence rate ratio between the groups
(II) assess the risk factors that are associated with the development of CRC

My statistical plans for the above are:

(I) Poisson regression (exponentiated estimate for IRR and estimated marginal means for IR)
(II) Cox proportional hazards model

However, I am not sure if the above methods are correct. i.e. should I consider death as a competing risk. If yes, how should I account for that in (I)? For (II), should I be using the competing risks regression (hence, estimating subdistribution hazards, instead of cause-specific hazards).

Also, trying to reference this paper: Higher rate of colorectal cancer among patients with pyogenic liver abscess with Klebsiella pneumoniae than those without: an 11-year follow-up study

I have yet to find a good use for a competing risk cumulative incidence measure. Such measures are interpreted as, for example, the risk of developing cancer before dying. I’d rather develop state transition models which give you highly interpretable unconditional state occupancy probabilities. One good resource is

If I am looking at incidence rate, instead of cumulative incidence, is it necessary to consider death as an event? Can we ignore if the event rate is small?

How do you define incidence rate? How small is small?