I should perhaps add, that I have installed the zookeeper packages (zookeeper zookeeperd libzookeeper-java) from testing into stable (bullseye), all other dependencies were already met with bullseye versions.
Also, according to https://www.slf4j.org/codes.html#StaticLoggerBinder and there the question "Failed to load class org.slf4j.impl.StaticLoggerBinder"... the files "slf4j-nop.jar slf4j- simple.jar, slf4j-log4j12.jar, slf4j-jdk14.jar or logback-classic.jar" are needed,... but any except for the latter is in place. All are in /usr/share/java. Though manually adding this to the CLASSPATH in /etc/zookeeper/conf/environment doesn't seem to help.