If you want to zoom in on clips, edit in a 1080 timeline with your 4K clips. That way you don't lose visual quality.
As for losing letterbox, your clip is not filling the full frame if you see letterbox, that disappears when you enlarge. You're using a different aspect ratio in your timeline, than your original clips.
In some cases you might see a bit of softening, and you are reducing a large number of pixels by exporting in 1080 - but having said that, it is still a decent workflow and the result will be pretty good. There is much more info on this forum about 4K clips in a 1080 timeline if you care to search.
The reason you are seeing letterbox is because your project is UHD 4K 3840 x 2160 which has a 16:9 aspect and the clip is DCI 4K 4096 x 2160 which is 256 pixels wider. In a 1080 timeline you can set the spatial conform to none and have a lot of room to scale, crop and zoom to fill the frame while keeping full quality of the 4K clip (theoretically).
If you want to zoom the clip and still have a letterbox effect, you should add an adjustment layer and apply the letterbox effect to this adjustment layer. This way the letterbox is unaffected by the zooming and will persist throughout your timeline if you so desire.