nothing is permanent on the internet, but any numeric observation ID in iNat will probably outlast any chat message you have with someone. i don’t know if the numeric ID will be the primary ID used by iNaturalist 10 years from now (or if the UUID or some other system will become the primary ID), but i would think that any numeric ID that had already been created would most likely still be accessible using that numeric ID, even if was no longer the primary ID.
here’s a previous discussion about the permanence of observation IDs: https://forum.inaturalist.org/t/is-the-observation-number-permanent/11887