Is running SQL Server 2022 with a reduced compatibility level of SQL Server 2016 (130) a supported configuration by Microsoft?
The supportability applies to the SQL Server version, not the compat level. Thus, using SQL 2022 with compat level 130 is supported.
Are there any known limitations, performance implications, or feature restrictions associated with using SQL Server 2022 in SQL Server 2016 compatibility mode?
Yes. When it comes to features, the new function generate_series will not be available to you. There maybe others, but this is the one I recall on the top of my head. But many new features will be available to you, for instance ledger tables and the function string_agg.
When it comes to performance, you will run with the optimizer features of SQL 2016, so you will miss out on batch mode for row store, scalar function inlining and other optimizer enhancements. Thus, you will not get the full benefit of SQL 2022. Then again, if you are on Standard Edition, you would not have access to all optimizer enhancements even with compat level 160.