This is worrying to hear. The company I work for has the self-hosted version which performs very slowly and seems to be gradually getting worse.

We are apparently moving to the cloud version soon, and it’s being sold to the users as the saviour for all the performance issues we’re encountering.

In my experience, cloud is faster.

On-premise was designed for LANs. It does not traverse the internet well.

That doesn’t make any sense.

Over-the-wire latency is the tiniest fraction of the time spent in a transaction with Jira (and Confluence). Most of their slowness is due to poor implementation in the client and backend, i.e., their applications.

Your JIRA instance probably needs to be hosted on more powerful hardware. In my experience, JIRA on-premise is way faster than JIRA cloud (but I do prefer the new UI in JIRA cloud, though that's a matter of preference).

As an example, Atlassian themselves still use the on-premise version, and it's really snappy: https://jira.atlassian.com/issues/

In my experience, which includes both the self-hosted and cloud version, this isn't true. They're both slow, bloated, and have terrible UIs.