There is a clear legal concept for this scenario defined in
CRS/AEOI, called Stateless Persons. On contrary, an entity is never stateless. If an entity fails to fulfill residency requirements through PE rules or other laws in any country, it is resident where it is incorporated.
Every bank may have their own risk-based approach to Stateless Persons but the CRS/AEOI model gives clear guidelines. Some banks are refusing stateless persons altogether and there's nothing illegal about such approach either.
Unless the bank has their own risk-based approach, they generally default to following:
1. Ask the client to provide sufficient evidence of stateless status (bank statements for last 12 months from their own records may suffice)
2. If they cannot provide plausible evidence of stateless status, proceed to close the account
If you tell your bank you are tax resident in a country where you renounced your
tax residency, you are shooting yourself in the foot. If the tax office receives this claim, they will happily treat you as such. Start by showing your bank the form of tax residency renunciation and provide sufficient proof of frequent travel.