A quick note, the screenshots you provided are very small. As a result, the information from two of the four screenshots is not legible.
That said and to the best of my knowledge, the source of the resolution/scaling behavior is a limitation of macOS on Macs that have an Apple processor (M1, M1 Pro, M1 Max, or M2), in that macOS is not enabling HiDPI mode for the Eve display connected to the Plugable adapter. This behavior apparently does not occur when using Macs with an Intel processor.
Again to the best of my knowledge, this can happen in a number of different scenarios, even when products not based on DisplayLink technology are in use.
Some posters in this forum have reported success using the application 'BetterDisplay' (formerly known as BetterDummy) to create a 'dummy' mirror display to work around the issue -->
https://github.com/waydabber/BetterDisplay
Keep in mind that your results may vary, and that 'BetterDisplay' is a 3rd-party application which is not supported by DisplayLink or to the best of my knowledge by Plugable.
NOTE - You mention the inability to use 144Hz refresh rates via the adapter. According to the specifications Plugable provides for the adapter -->
https://plugable.com/products/usbc-6...specifications the maximum refresh rate supported is 60Hz.