As others have said, it's not a necessity to use a mixer in between your signal sources and a multi-channel audio interface.

I've been doing home recording that way for nearly 20 years - never had a mixer in the system.

Mixers can be useful, but not necessary. And since they are powered and so forth, they do add a source of noise into your recorded signal chain - if that matters to you.

Depending on how many channels you want to record, you need to consider how many condenser microphones you will simultaneously record for separate processing in your software, as these need phantom power - The number of phantom powered channels in an audio interface is probably the main source of expense, as a general rule of thumb.

If you want to bus down drum tracks into two-channel pairs - then you can use your existing mixer to provide power to those condensers and record drums by themselves as a two track then overdub other stuff - that's a way of working that is also well-worn and proven out - and the interface will be less expensive.

Best wishes and welcome to the home recording world.