IMO, such should be low on priority list.!?
However, my opinion comes form the remote IoT world, where bytes cost more.
I would see the the webserver as @Mike suggested would be a good use of resources.!
We implemented such functionality via OTA connection, where TeraTerm is the client.
Essentially an OTA terminal environment. This environment is only used when there is some ‘Deep’ rooted problem, where such problem is totally unknown. Requires continuous connection.
Otherwise, normally, we OTA commands to remote device (hand-rolled webserver) to gather debug data…based on what are previously known possible problems. Requires a NOT continuous connection.