The "legacy" (pre 2019 or so) web interface for Google Contacts had a way to select (and de-select) the "My Contacts" label. This gave the user some measure of manual control when contacts are miscategorized. The current (2020) interface does not have that "My Contacts" label visible as a selection choice in any interface that I am currently aware of.
It used to be that if you unchecked the "My Contacts" label (when the option to do that was available), the contact would then be listed in "Other Contacts" in the "new" interface. It was a useful distinction - I could keep the noise out of my main "My Contacts" list, but still have a record of rarely used contacts so that a couple years from now (for instance) when I get a call or text message, I could still have a record of it to refer to.
I have not found (yet) a way to "move" contacts in and out of "My Contacts". For a while, you could choose the legacy interface. That option is no longer available, or I have not found a way to get at it.
I did find a way to do "move" contacts out of "My contacts". There is a 'Hide from contacts' option for each contact in your 'My Contacts' list in the contacts.google.com web interface. That will move the contact to 'Other Contacts'. I don't see such an option to do that with Google's current Android app version of 'Contacts'.