Fuzzy / Adaptive Resolution on Playback

If by "full render" you're referring to allowing After Effects to cache frames for Preview, then yes, we need to wait for the frames within the Work Area to be cached at the current resolution (the render status line turns green along the Time Ruler in the Timeline).

If Composition > Preview > Cache Frames While Idle is enabled, After Effects will cache the frames for you after the Idle Delay preference setting (it defaults to 8 seconds) expires.  If Cache Frames While Idle is disabled After Effects will cache frames as we move the Current Time Indicator or upon starting a Preview.

If the render time seems slow, expand the Render Time pane to view which Layers are taking the longest to cache at the current Comp resolution.  You may be able to make adjustments for faster renders, but you'll likely need a more powerful workstation.  Take a close look at Hardware recommendations for Premiere Pro and After Effects.  It's usually helpful to confer with others who do similar types of work in After Effects as to what hardware you could be using.  For example, if doing UHD broadcast promo graphics, I'd try to be working on a system with 192GB of RAM, 4TB ultra-fast SSD storage, and 3.2 GHz 16-Core Intel Xeon W or faster with the expectation of being able to work frequently at half-resolution and full-resolution.  If working on, let's say, an 16GB M1 13-inch MacBook Pro instead, I'd expect to work at Quarter Resulution most of the time, skip frames during Previews often, and wait longer for full-resolution UHD Previews and renders.