I’ve worked with many switches. I have not encountered a 10g switch that will negotiate to 10m. 100m is not automatic in most cases. These very old protocols are very different from modern 10g-100g. So much so that the transceivers may need to load a completely different firmware to even understand it.
Ok. Most of my experience the switches will have 2 modes for each port: 1G/2.5G/10G/25G/100G or 10M/100M/1G/2.5G. This is typical for datacenter switches. Found this out when my trusty 10/100M USB dongle couldn't establish link. I needed to upgrade to a 1G USB3 dongle.