With Omicron representing about 98% of current COVID-19 cases, does this reduce the need to keep vaccinating people, or will the prior strains still keep circulating and eventually reach everyone?

The latter is a very real possibility, much in the same way there are many endemic pathogenic organisms that seem to be lying in wait for a victim. What is happening, of course, is they are simply spreading slowly, but somewhere at all times there are some infected individuals and the odds they will spread it to someone else are high enough that new cases can keep spreading, albeit slowly, and enough sites of active infection are present to keep the organism jumping from host to host and not dying out altogether, which is obviously desirable to happen. We see that this virus is infectious enough that it will persist and eventually there will be enough natural immunity that very few will have a problem, other than those with significant comorbidities, like extreme age and other serious health conditions, where picking up an infection with COVID-19 might well do them in. So we see a place for routine vaccination for people at risk of serious complications should they become infected in the future.