See:
Release SQLite3 gem - precompiled for SU · MSP-Greg/SUMisc (github.com)
Both 1.4.0 and 1.4.2 (actually master as 2020-12-09) are available supporting Ruby 2.2 thru 2.7.
Re SketchUp 2021, I ran all the tests within SU 2021 (Ruby 2.7), and they all passed. See notes in the link above.
Both gems are pre-compiled using MSYS2/MinGW, and all included Ruby versions pass the sqlite3-ruby test suite when used with stand-alone Ruby. Note that the Ruby in SketchUp 2021 is a mswin build.