It’s disappointing that any web host should upgrade your database without warning like that.
Currently kiwitrees is not compatible with MySQL 8. I wasn’t planning on changing that before mid- 2022 as there are other priorities.
I can investigate fixing the SQL_CACHE issue as that does not negatively impact any other sites, but I cannot yet tell you what other issues might arise even once that is fixed.
I will try to release a 3.3.10 version of kiwitrees during November with the SQL_CACHE Included.
There is no earlier or simple fix I can offer you. Hopefully your web host can offer a service that uses MySQL 5