Is there a specific metric we can follow on-chain, or how we can observe or infere a chain reorg has happened?
cardano-db-sync instance I see a one block reorganisation a couple of times a day. Two block reorgs maybe once a week or month and I have never seen a 3 block reorg. That does not mean they don't happen, just that they are rare.
There is no on-chain metric which would show reorgs. Furthermore different parts of the network may see different sets of reorgs. That is simply the way distributed ledgers work.
The only "truth" is for blocks which are unlikely to be reorganized (more than 5 blocks deep and less than 2160 blocks deep) or cannot be reorganized (more than 2160 blocks deep).
If you wanted to view reorgs, you could do if from the logs of a running node, but even then you would only see reorgs that your node sees. There may be other reorgs on other more remote (not remove geographically, but remote in terms of network connection and latency) parts of the chain.