Is the only reason for having AD is to provide DNS services?
If so, implement private DNS zones instead.
If not, you can still actually use private DNS zones in AD environment. For details, refer to https://mwesterink.wordpress.com/2023/03/09/running-active-directory-domain-services-using-an-azure-private-dns-zone-and-an-azure-dns-private-resolver-does-it-work/
Otherwise, deploy additional domain controllers in other regions. Regarding the sizing, that would depend on how busy your environment is, but considering your description, this shouldn't be a significant factor. You should actually do this anyway to provide sufficient resiliency.
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hth
Marcin