Switching the entire live website to TwentyTwenty or Storefront is not possible at the moment because the site is active and receiving customers.
However, the issue only happens with WoodMart, and it is specifically related to the shop page product loop.
The products appear normally in the backend and on single product pages — they only disappear from the shop archive.
Also, the issue happens randomly and gets fixed temporarily after clearing WoodMart theme cache.
This clearly indicates a WoodMart cache or loop rendering issue, not a general WordPress problem.
If needed, you may create a staging site and perform any testing there.
Please proceed with investigating the problem on your side.