Example of tested JSON and its path:

{"f$o":"bar"}
$.f$o

If you will test it, you will get an error:

cannot extract value from json by path "$.f$o": unsupported construct in jsonpath starting with: "$o"

https://git.zabbix.com/projects/ZBX/repos/zabbix/browse/src/libs/zbxjson/jsonpath.c#205

I assume such object names were not considered when writing function "jsonpath_next":
https://git.zabbix.com/projects/ZBX/repos/zabbix/browse/src/libs/zbxjson/jsonpath.c#522

How does it work for "jq" tool, just an example:

# echo '{"foo":"bar"}' | jq '.foo'
"bar"

# echo '{"f$o":"bar"}' | jq '."f$o"'
"bar"

Some web based tools, like https://jsonpath.com/ do not require any special syntax/formatting/escaping for the example.