[clangd] Move logging out of LSPTest base class into a separate one.

This was causing TSan failures due to a race on vptr during destruction,
see
https://lab.llvm.org/buildbot/#/builders/131/builds/6579/steps/6/logs/FAIL__Clangd_Unit_Tests__LSPTest_FeatureModulesThr.

The story is, during the execution of a destructor all the virtual
dispatches should resolve to implementations in the class being
destroyed, not the derived ones. And LSPTests will log some stuff during
destruction (we send shutdown/exit requests, which are logged), which is
a virtual dispatch when LSPTest is derived from clang::clangd::Logger.

It is a benign race in our case, as gtests that derive from LSPTest
doesn't override the `log` method. But still during destruction, we
might try to update vtable ptr (due to being done with destruction of
test and starting destruction of LSPTest) and read from it to dispatch a
log message at the same time.

This patch fixes that race by moving `log` out of the vtable of
`LSPTest`.

Differential Revision: https://reviews.llvm.org/D98241