I don't think CBDC will be a competitor to bitcoin in real use cases, but the government will work on CBDC to be the first as an alternative solution to fiat. Bitcoin will continue to be used by anyone concerned with privacy and decentralization, so CBDCs may not appeal to most bitcoin users, let alone maximalists.
CBDC is a centralized project initiated by the government. This is one that goes against the idea of bitcoin likely not attracting much interest from users other than just using it for specific purposes. The idea of using it is the same, it is an alternative.
There's no competition on these 2 currencies as they have different nature and use cases.
CBDC is like the digital fiat currency of the government and so it is indeed centralized.
With btc, people have more freedom in utilizing this top coin. They don't need to worry about
the government lurking their activities if they know how to handle their transactions discreetly.
So yes, people will use these 2 currencies, but on different circumstances depending on the situation they are in.