Prompt bookkeeping introduced in 66ca6252 is not thread-safe, whilst the
logging environment is multithreaded: leave this feature only in main
(transaction) thread.

Closes #8124

NO_CHANGELOG=<gh-7169 was not release yet>
NO_DOC=bugfix
NO_TEST=<hard to make Tarantool flood log from multiple threads using
         current test harness>