Hello @Alexandre and @kmkevin
I have the same exact issue, it was reported earlier today from one of my users (a simple resaerch was taking way too long) .
I updated Control Panel to 3.1.1.467 and Community server to 12.1.0.1760 two days ago (28th march) however, Document server still on 7.0.1.37, mail Server uninstalled.
So at first glance, when researching for a Folder or a Document it is either not working or taking way too long and we get a timeout.
A Javascript Error is prompted :
I was wandering if an indexation (dunno if this is the english correct term) was occuring or was faulty, and took a closer look at the control panel to see if full-text search was activated.
Then i got the same error as @kmkevin
On elasticsearch’s logs (elasticsearch_deprecation.log to be precise), the last entry is this
"The default behavior of disabling security on basic licenses is deprecated. In a later version of Elasticsearch, the value of [xpack.security.enabled] will default to “true” , regardless of the license level. See Set up minimal security for Elasticsearch | Elasticsearch Guide [7.16] | Elastic to enable security, or explicitly disable security by setting [xpack.security.enabled] to false in elasticsearch.yml
"
by the way date/time in this log is exactly when the server was restarded due updates two days ago.
In elasticsearch.log , a huge list of errors " almost every type like this pattern : [o.e.d.PeerFinder ] [id(will provide in pm)] address [127.0.0.1:9301], node [null], requesting [false] connection failed: [][127.0.0.1:9301] connect_exception: Connection refused: /127.0.0.1:9301: Connection refused
Trying to connect from port 9301 to 9305 with no results.
I hope we can fix this and thoses additionnal informations help you.
Take Care 
