I am currently using SQL Server Express edition, and am thinking of upgrading to SQL Server Web or Workgroup edition.
My question is what restrictions will I experience with the introduction of CAL licensing
CAL licensing isn't required for either Web Server edition or Workgroup edition and may not be suited for you depending on size.
Unfortunately, Workgroup is being retired and Web edition won't even be available outside of the SPLA (Service Provider License Agreement) per Microsoft
As for restrictions with CAL licensing, it's hard to say without your specific use case of SQL Server. If you have a web application Microsoft CAL based licensing can literally require a CAL for each and every web visitor (assuming you purchased it that way for some reason). However, that's why per processor licensing and SPLA licensing exist.
If you want a more complete answer or more details, please update your question to include specific details of what you are attempting to achieve.